I would add some way to sort and filter items in the “Add item” selection in the character sheet. I think there should be at least an item level filter and a sort by price, name and level. For example typing “shield” shows every possible shield sorted by name. This isn’t very practical for characters with specific levels. It should allow ranges of levels or selection of multiple levels. For a 1st level character the best would be to search 0th and 1st level items.
I get that the main way of finding items is through game compendium, but some simple search options should be available in the character sheet as well. Filtering by item type would be cool, but I get that it will maybe clutter the UI too much.