Specifically Scene 4 of episode 4. It gets halfway through and crashes.

Am I to assume there is no way to skip it? It kind of sucks because this little hiccup is keeping me from playing the chapter and then moving onto other chapters

Is this about lego star wars complete saga?
You mean rescue the princess chapter 4 in episode 4 intro?
I have no problems with it, do you use any codecs?
Also most of the video or graphic settings i turned off ingame menu try doing that and then play that chapter, also i am currently using k-lite codec pack if that will help.
Though am not sure if one needs codecs to play movies ingame.

all the Lego games have gotten buggy on my PC as of late.

I've moved onto to other things, but thank you.

The games didn's age well. All 2000-2010 games are kinda buggy, since DirecX was kinda new and many programmers did a LOT of bad things.
Also it seems, some of the recent Windows Updates were not in favor of the early Lego Games.

I also experienced crashes, it became very frustrating.
...

Edit: Well it runs quite good by now.
3 steps:
1. use dgVoodoo to get rid of the crashes
2. set the game to windows XP compatibility mode (or Windows 98 SE or Windows 7, see what works best for you)
3. make sure energy saving for your processor is disabled. Core 1 must run at full speed (turbo or anything like that is not required, the game is not THAT new)

Now and then the game hangs, when the system is doing something that requires core 1 or if an application tries to grab the focus, but thanks to dgVoodoo that won't cause the game to crash.