So I know the rules-as-written specify that the side board from MoM is only used for the Rise of the Elder Things AO and one specific Prelude card, but would there be any problems with just using it all the time? I really like having it around.

No probs in using it. Done several times in the past, it always worked. Just remember to add the clues and the gates related to the side board, and you're ready to go.

Is it not annoying… looking for that clue everytime un a clue back?

Just use them as usual only if it come as random location indicator discard it and draw new one. Or?

I've only played with the side board once, so could be missing something, but I don't get the impression you'd be going there for the clues due to not drawing AO research encounters for them.

Personally, I kinda like the idea of keeping it separate - maybe not exclusively for the Elder Things, but I like this idea of expansions not overwhelming the game!

Glaurung,

indeed, you can keep all the gates and the clues mixed together. If you don't play with the sideboard and you draw one clue / gate that should go there, simply discard it and draw a replacement. Just beware of when you're about to run out of clues / gates, but it's easy to keep track of.