Considering John Carmack's on the zenimax pay roll and has stated that he was more then willing to let Bethesda share there technology I don't see how this would be a huge issue. Hell we might get a less buggy game if they use id Tech 5.
Having id on their side for their tech expertise will certainly be a big help to Bethesda. (And I'd also be suprised if they didn't make use of Tech 5 - if for no other reason than since Zenimax owns id, it's going to be more financially feasible to use what is now technically an in-house engine than stick with Gamebryo.)
As far as bugs go, though - that's not really anything to do with the engine they used, but the coding they did for the game (which is still basically C++ when you go right down to it...)
I think people get a bit confused on just what role an engine plays in game development. (Not saying anyone here so far doesn't understand, but just for clarity's sake:)
The difference between using one engine or another when making a game is roughly equivalent to whether I design a webpage in Dreamweaver or GoLive. Or whether I make an image using Painter or Photoshop, Flash or Illustrator. Or whether I make a 3D model using Maya, 3DStudioMax, or Blender. It's just a set of tools. Some can be better at different things (in the case of engines, how the image is rendered, etc,) but the efficiency of the coding in that web page; or the end result of an image, still come down to familiarity with those tools and the skill of the user. In fact, it's very much like using any of those other programs. It's a common suite of tools that all of the design team use to create what they're doing.
For the end-user, the videogame player - the only thing that really matters in terms of which engine was used lies more in which reflections you think look better, or how the game handles level of detail transitions, etc. Things like bugs, animations, etc, are much more related to the actual coding and design of the game itself than the engine that was used. (In the same way that I can botch a script just as easily in Dreamweaver as any other HTML coder.) The actual graphics themselves and such generally have much more to do with the modellers, texture artists, art direction team, and animators than it does the engine that was used.