Various Ideas

More Individual Statistics:
Saves - Applies to Goalkeepers only. This statistic is already recorded during matches, but it is not displayed anywhere.
Clean sheets - Applies to Goalkeepers (and possibly defenders) for not allowing a single goal during a match. Simple enough to implement, I believe.
Pass Efficiency - Applies to everyone. This statistic is already recorded on a team level, and would be useful on an individual level.
Club assists, saves, and clean sheets (all seasons) visible on the player profile.
Career (all clubs) statistics.

Inactive List or Expanded Squad Size
An inactive list would basically free up a roster spot for when a player is injured.
Can also be used for healthy players, but with consequences:
- A healthy player placed on the inactive list loses a considerable amount of morale.
- Players are not allowed to train or participate in games while on the inactive list.
- Players' condition decays over time, same as if they were injured.

A slight increase to the squad size is another alternative, which other people have suggested before. I think a squad size of 24 would be more than adequate.