What things are missable in disc 1 of Final Fantasy 7?

Solution 1:

I don't think there's much more you can do for her once you have her ultimate weapon and final limit break.

As for other missable items/materia, there's a guide on GameFAQs that details them.

Solution 2:

Get her to level 100 and obtain all her limit breaks and weapons, then move on. Accessories, materia and other similar collectibles aren't character related, so you can collect them later. I think the other characters' limit breaks and ultimate weapons won't be available on the first disc, so you can't use her as part of a fully maxed out team.