What's up with Computer ID Suggestions in Identify Mode?

That depends on what settings you use. This sounds like you’ve got it set to show Observations (which is what I mostly use myself, but not always), but if you choose ‘Visually similar’ it should show up to ten CV suggestions based on the current ID (so within the genus for a genus or species-level ID, within the family for family level, etc.). If the observation has no ID, it will guess from any kingdom but you can also choose whatever level you want it to look at in a way you can’t in the individual observation pages.