Swollen segments
I'm not sure if there's a proper name for this particular problem nor am I sure exactly what causes it though I've seen evidence that it could be internal injuries caused by a fall. I had a bronze millipede which I accidentally dropped and his rear end caught the edge of a table. Not wanting to stress the millipede further (I'd just received it in the post) I put it in its new enclosure. After a while I noticed its back 10-15 segments were swollen and the legs seemed paralyzed, eventually I noticed a prolapse so it was then I took the decision to move him into a sterile container with food and water. The millipede in question did recover and lived for a number of years after this took place. I have no idea if anything can really be done to help millipedes that suffer from this other than to make sure they are living in optimal conditions.

Missing legs
When you look at all but the most perfect millipede you'll likely notice the loss of a few legs. This doesn't hinder the millipede much as you can imagine - they have plenty of legs to spare. Problems can arise when a millipede loses a number of legs from a particular area of its body such as the front or back. If it loses too many legs from the front it will have serious difficulty in getting around and if it loses too many from the back it may drag its rear. To be honest there isn't much you can do about legs that are already missing and the millipede won't even be able to regenerate them after a moult like some other inverts do. This brings me to my next problem...

Foot rot
I've noticed a few millipedes I've received seemed to have been suffering from something which I've been calling "foot rot". I suspect this is a fungal disease which results in loss of parts or whole legs. While damage caused can't really be treated the condition can be controlled by lowering humidity in the cage, in the worse cases the millipede should be removed to a container filled with slightly dryer sterile soil as the fungus seems to do well in damp conditions.

Fruit flies
Without a shadow of a doubt these things are the biggest pain in the arse I have had to deal with when keeping millipedes. They breed like crazy in millipede tanks and there is not an awful lot you can do about them. One thing I have noticed is that when I've introduced woodlice to my tank I get less fruit flies breeding there. At the moment my millipede tank is fruit fly free (try saying that fast 3 times) after I introduced woodlice around a month ago. My giant snail tank on the other hand is like a great big fruit fly rock festival. If you find yourself with fruit flies try and change as much of the substrate as you can and get some ordinary garden woodlice in there too.

Fungus
Sometimes white growths or hairs will appear on the millipede's exoskeleton, this seems quite rare but I imagine it would be down to conditions being too damp. Don't attempt to clean the fungus off the exoskeleton as this could weaken it further. Increase temperature if possible and decrease humidity, this won't cure damage already done but it should prevent the fungus from spreading to fatal proportions.

Mites
There are a few mites you have to be aware of when dealing with millipedes. The larger millipedes often carry dark mites on their bodies which move around the millipede while eating bits of dirt etc. These mites are "good" mites and should be left alone as removing them will be stressful to the millipede and will do it more harm than good. A good millipede mite can be seen on this yellow faced millipede's cheek...

The other type of mite is smaller, white in colour and doesn't often move around on the millipede's exoskeleton. These are the mites you have to worry about as they will puncture the millipede's exoskeleton and drink the fluids. Some steps to get rid of these mites include drying the millipede's container, obtaining predatory mites, putting the millipedes in flour and other such things. Personally I've never had a problem with mites but if a millipede seems to have a very bad mite problem I'd keep it in a sterile container and change the substrate every day until the mites have gone. To remove mites attached to the millipede use a cotton bud dipped in Vaseline (keep this AWAY from the pores along the side of the millipede's body and the mouth). Your other option is to buy some predatory mites which will eat the millipede mites and also any other little nasties that are in your tank. Once they have devoured all the bad mites in your tank they will turn on each other eventually leaving you with a mite free tank. It's taken me a while to track these down for sale in the UK but I finally found them available HERE