First glitch, the most annoying one.
On the newer systems, there is an annoying music bug, where from time, to time the music freezes, and costantly loops the same part.
Second glitch, the most strangest i enountered.
on my latest playthrough, in the Final Battle (Naboo Hangar), where you fight Dart Maul, alongside with Qui Gon Jinn i encountered a glitch, where there was Maul fighting Qui gon, and a second Darth Maul standing in the middle of the Hangar, doing nothing. I wanted to kill Darth Mauls clone, but it was invincible, so i went fighting the real one
Third glitch, the most coolest and desired by everybody.
You can pass through the falling platforms in Level one (Trade Federation battleship), though it is hard to do, and you need some skill, to achive that. I menage do do this in the demo version of Phantom Menace. I dont know if it is possible in the full version. I also heard, that it is easier to do in the PS1 version. You can see a video on Youtbe, where some guy is doing that on the PS1 version. There is nothing special behind the falling platforms, just a squared area, with closed door. There is also a place, where you can fall through the level in this area.
Fourth glitch, the most useless one.
Pass the falling platforms, in the vent area (Where your ship is blowing up) You can jump on that metal boarder/fence, close to zapping droids entrance. (You have to be close to the entrance though, otherwise Obi Wan slides down).
Now, this is not really a gltich, but it is also worth mentioning. You can easly beat Maul, when you first encounter him on the Desert. Just draw your blaster, move/walk constantly backwards and shoot him every time he gets close to you. How it works is, when Maul gets close and attacks, he stops and gets blocked by his attack animation, yet by constantly moving/walking backwards, you can escape his attack range. He also cant deflect blaster shots, when he is in the attack animation. All you need is a little bit of skill, to get the moment, when he attacks.
This is also not a bug, but remeber that little Gonk Droid, right at the start of level one. In the area, to the right from the conferance room, WHICH IS FILLING WITH POISONED GAS !! (Where you get a blaster, for the first time in the game) Well, if you wait a few minutes the Gonk Droid explodes, like a thermal detonator
Oh, and the last bug/glitch/oversight. On the final battle with Darth Maul, in the generator room, when maul attacks with his saber, you can notice that Obi Wan is bleeding. It is very interesting, becouse when Obi Wan or Qui Gon attack with their lightsabers enemies like, Maul, merc's or aliens, then they dont bleed. Personally i think, that it is cool
Somebody should make a mod, which would cause enemies other than droids to bleed, when attacked with players saber