It's too generous to say there were holes in the plot. That presupposes that there was a plot. The story doesn't hold together in any way. Saying there are holes in the plot is like saying there are lakes between the Hawaiian Islands. There's just one great big hole with a few isolated fragments of plot scattered within it.
I mean, the first 15-20 minutes of the film seem to be telling one story: Indy gets in trouble at a military base, falls under suspicion due to the rampant paranoia of the McCarthy era, and loses his job. Now, in the original Frank Darabont script, that actually led somewhere. It had relevance to the story that followed. But in the finished film, from the moment Mutt arrives and addresses Indy on the train, none of that is ever mentioned or has any connection to the story that takes up the rest of the film. It's like we're suddenly in a completely unrelated movie.
Sure, in the final minutes, we see that Indy hasn't only gotten his job back but has evidently gotten a promotion, but there's not a single word about how or why that happened. It can't be the result of his crystal-skull investigation; he didn't bring back any evidence, any artifacts, anything except a story nobody would take seriously. He just got a random happy ending because it was the end of the movie. It was completely disconnected from the rest of the film. That's horrifically bad story structure.
And there aren't any real character arcs either. There's the guy who seems to be an ally and then a traitor and then a double agent and then a traitor lying about being a double agent, but it's just random switches to complicate events. Spalko is presented as the main villain, but at the end she seems to be only a seeker of knowledge and her fate appears more like transcendence than destruction. Mutt is resistant to the idea of Indy as his father until he suddenly comes around for no clear reason. Marion, this wonderful character returning to the series after far too long, is almost totally wasted, reduced to nothing more than the love interest, which is an even smaller role here than it was in the original film.
People complain about the aliens, but the use of aliens was the least of this film's problems. A solid script could've integrated that concept effectively. After all, Indiana Jones is about mythology, and UFO beliefs are a modern mythology, a New-Age belief system that from a cultural and psychological standpoint is functionally identical to a religious cult. And the '50s were just when that cult was getting started. So that part could've been managed. The problem is that the script is simply incoherent. Lucas had an excellent script to work from, the Darabont draft. Darabont's version had its flaws, like too many villains, a lack of a standout primary villain, and some action scenes that were too cartoony and overdone; and it lacked the Mutt character that Lucas insisted on having. But those problems could've easily been remedied in revisions. Instead, Lucas threw out that script altogether -- aside from keeping the McCarthyism stuff at the beginning even though it no longer had any meaningful followup -- and what replaced it was simply inadequate. It was just a string of set pieces with nothing really holding them together.