Also one other tip - when you have 2 surfaces that share a common edge and you want to glue them together, it's usually best to use the Edit > Join command to do that rather than Boolean Union - Boolean union is focused more on combining 2 shapes together where they are actually intersecting one another and need to have some area removed from the combined result.

If you know that you only want to glue touching edges together and don't need things to be intersected and have material removed, the Join command will only do that kind of gluing and not try to do intersecting.

It may be possible that you've got some slivery pieces generated because of using booleans where they're trying to cut things with each other in this case.

- Michael