Does everyone get this bug or does it depend on hardware/drivers? Is it just the first episode, or is the entire season affected?
I'm asking because for years and years I had something on linux/wine that may be related. My pet theory is that it was hitting a hardware limit in graphics card resources (memory, textures, whatevers), and doing so sooner than expected because wine had already consumed some of them for its directx->opengl translation thing.
I originally got season 1 directly from Telltale soon after release because I was very excited about Sam & Max coming back. Unfortunately the games suffered from graphical glitches when ran on wine that made them near-unplayable. Pretty much every character was invisible. Bosco was just eyeballs and a tongue. Sam & Max were visible but their geometry was distorted, with some parts stretching into infinity. This was wine bug #13612.
It wasn't just me, but not everyone suffered from this. I initially thought that it was an nVidia issue, but then it got reported on ATI too. Eventually I tried it elsewhere with pretty much the same software but newer nVidia hardware/driver, and there was no problem at all.
And sure enough, once I finally upgraded my system it started working fine for me too. I had only played through episode 1 in its buggy state. Telltale installers had online activation so I re-bought from gog.com and finished the season with no further issues, but didn't try episode 1 again.