Apologies if these ideas have been posted before (I did have a read through this thread and couldn't see anything quite the same...)
Thinking about how injuries are handled in the game (and I am not getting involved in the quantity / frequency debate) they are broadly black and white - player x is injured - will be out for x weeks - with caveat of maybe seeing specialist if it is severe (and you only get this option when he is first injured IIRC) or getting an injection - which means the player then plays one match but then is out for longer. That player is then out injured, and is essentially left to be forgotten about until he is fit.
With most injuries in football, managers are constantly balancing the need to get a player back as quickly as possible against the possibility of further injury setbacks, something which I don't think FM currently handles too accurately. Many times when I have had 6-10 players out, I have thought, if only I could maybe target 1 or 2 players to try and rush their recuperation, even if it does carry some major risks.
What I would like to see is greater physio manager interaction to determine the method of rehabilitation for the player. For instance, if player x has a sprained ankle, if it was left to nature / standard recovery, he would be out for around 4 weeks. However the manager could ask the physio to suggest techniques that could speed the recovery or enable the player to play e.g. taping, strapping, injections, sitting in an oxygen chamber, seeing a German specialist etc. In real life, with a moderately sprained ankle, for instance, after about a week you can get strapped up and play, but with the chances of reinjuring much higher than if you let it recover completely, and with physical and technical attributes likely to be reduced.
Here the rate in which players could recover / play successfully whilst carrying an injury could be dependent on the quality and quantity of your physios and or your finances (ability to send them to the best specialists). I'm not suggesting that a good physio could make the blind see, more he could use his skills to patch up a player more regularly and successfully than a poor one.
This feature could be tempered by players mental characteristics, e.g. Some players relishing the prospect of getting back quicker because they love the club or are fitness freaks, whether others may get upset that you are potentially ruining their bodies by trying to play them when they are not fully fit.
There should also be the ability for players with injuries such as Achilles tendonitis or back problems to play through a season or for a certain period before being sent off for treatment albeit with reduced stats where appropriate and / or increasing likelihood of getting different injuries, again something that happens in real life. I seem to recall this happened in very old versions of the game, so if it happens in this one, please disregard.
Players with injuries such as broken wrists, cut heads etc. should be able to play whilst still injured but with the risk of angering them depending on their mental characteristics (or pleasing them) as above.
Also players with colds, flu (if you are particularly sadistic) etc. should also be made to play but with reduced abilities (and risk of angering them) and risk of passing infection. At the moment the option of them being treated by a physio with less days off then sending them home seems a little odd (What do FM physios know about treating a cold or flu - so that patient recovers more quickly - that thousands of scientists don't yet know?).
I also third (or maybe fourth) the better description of injuries during matches – rather than 'he has picked up a knock he will have to go off.' From the prognosis of the injury (Again maybe dependent on quality of physio or the attributes of player) I should make a call on whether to carry on playing him and suffer any consequences from that decision.