I got to a part of the story where it seems that I've missed some spells. I do not want to get spoiled (nor do I want to spoil other players) and so I'd like to know, without spoilers (or with spoilers properly tagged), if any spells are permanently missable, or if I can learn some spells in any alternative ways.
According to my information there are three missable spells.
There is a time during the main quests where you can still learn two of these if you've chosen before not to learn them. This is only available if you don't progress the main story too much after this point.
Imperio and Crucio can be learned for a while afterwards by talking to Sebastian in the Undercroft. This does not apply to Avada Kedavra.
Yes - there are (up to) three spells that can be come permanently unavailable to you if you haven't chosen to learn them and then make a certain choice in-game that leads to the character who teaches you them being unavailable (in deference to the no-spoilers request I won't mention which spells, character or choice but it should be obvious once you get there). Choosing the other option means the spells remain available for you to learn at any point - including after the end of the main story missions are completed.
For those who are concerned with achievement hunting these spells don't count for the "Learn all spells" achievement/trophy, so you can't lock yourself out of that.