Right now I'm just watching "Second Chances" and I'm at 26:56 into the episode (where the two Riker's have their argument over the engineering "pool table"), and in the shot "yellow" Riker is extremely sharp, while "red" Riker looks like he's been through a couple of analog generations, even though it should've been a simple split screen effect (of course there could also be that the camera op never adjusted his focus for "red" Riker). Even with Betacam SP, it should've only been the third generation (second Betacam generation) from film for those two shots, and Betacam SP is rated for 6-8 generations before you notice any discernible loss. D2 I believe is closer to 40 generations. Even if Paramount used a different master for the DVD (even a DigiBeta or S-VHS copy from the late-90's), I don't think we'd see that much video loss, since it would've been sourced from the final edit master, and it probably would've only been one more generation away.
I don't remember that scene off hand, but if that pans from one Riker to another that shot could have been setup using the anamorphic trick they used quite a few times in TNG. It results in a rather blurry presentation, especially while panning. It was used for two Dax's in DS9 so maybe it was used here?