Continuing the hit points/hit dice discussion, Banesfinger's other example was of a low-CON, low level MU healing faster than a high-CON, high-level fighter. Again, this may or may not be a problem with suspension of disbelief depending on what you're trying to believe in, what kind of game you're playing. How you view hit points is going to affect how you view the problem.
If you are interpreting the attributes as quantitative differences between characters, this example is going to peeve you to no end. Especially if you interpret hit points as physical toughness. Logically, under those circumstances, CON should affect hit points and healing. Higher CON should mean more hit points and faster healing. You may need a house rule here that says you get, say, a 3d6 vs. CON roll every week to heal extra damage; the higher the roll, the more damage healed, unless the roll is higher than CON.
If you are playing in a gritty style, then this won't be as big a problem, because the real problem is hit points increasing with level. You're much more likely to take a BRP/GURPS solution for gritty and realistic play: hit points equals CON, hit points do not increase with level.
If you are playing a high-action style game and also interpret hit points more as luck than physical toughness, there is no problem. Scratch that: CON hp bonuses nag me. I'm tempted to disallow them except for dwarves and halflings, because that's their special feature. What I might do instead is allow high CON characters to reduce physical damage only, sort of like having a point of damage resistance.
But as for high-level characters in general healing slower than low-level characters, if I'm interpreting hit points as luck, it makes perfect sense. Having hit points means being able to turn deadly or crippling blows into mere scrapes and bruises. If you are in a lot of fights, eventually your luck runs out. High level characters have a greater capacity for luck, but they still recover luck at the same rate as everyone else.