These are all my interpretations of DotM's plot holes, not necessarily actual answers, but anyway
1) Okay, so Laserbeak wanted the Ukrainian guy to tell the NEST guy to send Optimus to Chernobyl and just poke around and see if they find anything interesting. This was presumably in the hopes that he'd get pissed off about the Ark engine part and complain to some US government people, who would then tell him everything that they know about the Ark, leading him to go to the Moon and revive Sentinel. Not a gamble that I'd place my money on, and it seems easier for Laserbeak to just directly tell Optimus that Sentinel is on the Moon, but whatever. Why was Shockwave there? Didn't he get the memo that the engine part was SUPPOSED to fall into Autobot hands?
I think Shockwave attacked so that the Autobots wouldn't suspect they were playing right into Decepticon hands
2) How did the Soviets get their hands on the engine part in the first place? We were explicitly reminded that the Soviets canceled their manned Moon landings, apparently because Dr. McDreamy convinced the American government that it wasn't very cost-efficient
Didn't one of the NASA guys say that the Soviets sent probes to the moon? It must've taken a small part from the crashed ship back to Earth. It stands to reason that the Cons had another guy working for the Russians, also screwing numbers around.
3) Speaking of which, why didn't the Decepticons want humans landing on the Moon anymore? They had already relocated all but five of the pillars.
To limit the number of humans associated with their cause, they just wanted the rest of the US/Russian space program to remain ignorant of their plan.
4) Why were Decepticons moving pillars around on the Moon if apparently Megatron and Sentinel were the only ones who knew about the plan?
That I honestly can't tell you. Was it explicitly said only Megs and Sentinel knew? Otherwise, Starscream or Soundwave might have told them. Soundwave in particular is trustworthy.
5) How did Shockwave's pet hentai tentacle monster robot get to Earth without anyone noticing? It doesn't seem well-suited to the "flying turd" method of atmospheric re-entry, given its size and inability to transform.
Uhm, eh... Perhaps he... and Shockwave came to Earth long before space detection systems existed. I believe Shockwave was already here for over a hundred years, according to the comics. He and the driller crashed in Russia, in an event that references an actual meteorite crash.
6) what's the deal with all of the Decepticons sleeping under the moon dust? How'd they get there? Why didn't they help out during the first and second movies? Why does the Space Bridge (an AUTOBOT technology) wake them up?
They were put there after news reached them of the Ark crashing on the moon. So they landed using those big transport ships, moved the pillars and without further orders, went dormant. Seeing how Jetfire has only slept for 30 years max (his alt mode isn't that old) they've slept long enough to shut down. My guess is, the space bridge emits energy that can reawaken them. After all, they're not ancient and critically injured, just sleeping.
7) If Sentinel invented the Space Bridge technology and is the only one who can operate it, then what were Jetfire and the Fallen using to teleport in RotF, and why did Jetfire call it a space bridge?
Jetfire was a Seeker, an ancient explorer of the universe, the Fallen is one of the Original Thirteen. These old ones apparently had built-in space bridges, with which they borught Cybertron to the Golden Age. The newer wave of Spark-born non-Seekers lacked this technology. Sentinel Prime managed to reproduce the technology into an external device anyone could use.
8 ) So Laserbeak can transform from a turkey skeleton into... a five-foot-tall approximation of G1 Arcee? What the hell kind of disguise is that?
He transformed into a kid-sized pink Movieverse Bumblebee. The idea is that Autobots are known to the general public by this point. By turning into a pink (little girls wuv pink!) version of one well-known good guy, he managed to convince that NASA guy's daughter to let him in.
9) Laserbeak sure seems intent on killing human collaborators who have served their purpose. So why does he continue chilling with Dr. McDreamy instead of killing him?
Dylan Gould made a deal with the Decepticons. He was a survivor and business man pur sang. I'm sure they agreed to keep him alive because he kept providing the Decepticons with personell, vans to transport the pillars and a place to stay. Laserbeak has been a working partner with Dylan for years and mr. Gould sure seems glad to work with them, as opposed to terrified.
10) When Megatron and Sentinel decided to rendezvous on Earth, did they know that that's where the Cube was, or that that's where the sun-blower-upper machine was, or what? Megatron seemed pretty hell-bent on finding the cube in the first movie, but if he came to Earth because that's where the cube was, why did he even bother with the space bridge nonsense? Why not just "Yo Sentinel, I know where the Cube is! Let's go"? Same thing with the Matrix and the sun-blower-upper, but worse, because the plot of RotF already makes no sense even if you don't try to fit it into the other movies' plots.
Megatron at least knew the Cube and the Solar Harvester were there. The cube had traveled to Earth, because it had once been a colony and a Harvester was built on its surface. Megs probably wanted to use both the Cube and Earth's people to create an enormous working force to reconstruct Cybertron. The whole RotF story isn't as well connected.
Basically nobody knew the Matrix could revive TransFormers like the Cube could. ANd that's because it actually couldn't do that. When the Cube was destroyed, its knowledge and power were transferred in two shards and Sam's mind. The shards were used and Sam transferred the Cube's power and knowlegde into the Matrix dust after reviving. From that point onwards, the Matrix acted as a new body housing the Cube's essence. Before all this, the Matrix was just a powerful key and the Fallen's plan to find and use it seems to clash with Megatron's plan to enslave rather than destroy Earth. Perhaps, with Sentinel seemingly dead in RotF, Megatron opted to destroy the Sun (and Earth) and kill Optimus. Back then, they didn't know Sentinel could be revived, so they took the other option.
11) "Hey guys, guess what? I just learned that about 10,000 years after I crashed here, and about 50 years before I woke up, the guy that I was supposed to rendezvous with finally showed up! Problem is, the Decepticons who have been dicking around on the Moon for no apparent reason tell me that he's dead. So all we need to do is get the cube sliver that the humans are keeping safe in that military base... wait, what do you mean, 'you used that one on me already'? Well, are there any OTHER shards? Oh, good. Let's get that one and use it to bring Sentinel back to life. No, don't send Ravage again, it's someone else's turn. No, not you, Starscream. You're a whiny little bitch. Soundwave? I prefer that he remain in space doing absolutely nothing that could possibly help us. How about Devastator? No, not the tank, the one made from six other Decepticons. Oh, one of them got scrapped for spare parts? Screw it, just send that little blue guy. No, his eyes do NOT look vulnerable to blowtorches! Yes, of course I'm sure he's loyal to the Decepticon cause..."
I ROFLed at this. But it's true, they don't seem to care for the mission if they send Wheelie. In the end, it doesn't really matter though. Both shards are used (the second on Jetfire), leaving them with no options, until Sam transfers the Cube's power to the Matrix and increases its abilities.
12) Okay, the entire human population of Chicago has either fled or been vaporized. Conveniently, this is also where Megatron, Sentinel, the Control Pillar, AND the last surviving human collaborator are located. If only we had some kind of weapon that was capable of destroying entire cities... nope, gotta send in some Navy SEALs and a kid with a goddamn grappling glove.
Even if all the evil dudes are together in one city, would you nuke it? Several scenes show lots of survivors still hiding in Chicago, long after it has been 'sealed'. It hasn't been wiped out, just locked from the outside world. The USA wouldn't just obliterate its own people and cities to get to the baddies.
13) The Decepticon airships... have pilots? Dude, Decepticons don't pilot flying machines, they TURN INTO flying machines! Who wrote this crap?
Yes, they have pilots. I don't think those drones/protoforms can fly. And even if you can fly and shoot missiles out of your body, it's smarter to use something else. You won't get hurt if the ship is hit, after all.
(-) Ugh... this probably isn't even half of what's wrong with the plot of DotM, but let's take these questions a few at a time.
Bring them on, I like these questions