It might be a problem with Construct itself, like if there were any problems during the installation (did any windows pop up that seemed strange?). If that IS the case you might need to re-install or update or do whatever to Construct, to see if it can settle in your computer with more stability.
Or it could be you're using some wonky files for sprites, though I highly doubt that. I myself use bitmaps and they work peachy.
I've never heard of crashing due to sprite deletions though (my crashes have been kinda isolated events).
EDIT: in fact, the big topic that says "READ THIS IF NEW" in this forum says:
[quote:2z5yb9b2]4) If it crashes, it's a bug! Ideally, software should never crash. A crash indicates the program has failed, not the user. In this case, post a bug report.[/quote:2z5yb9b2]
As far as the "unexpected movement" thing, you'd have to be more specific, because there's no way to gauge what you mean by that vague statement. If you know how to post a .CAP, that might help (I don't personally), so one of the pros can look at what's going on.