Re: predictive value of "level".
Level (defined as meanskill - sigma) isn't supposed to be a predictive measure anyway, so why would it be predictive? It's just notational shorthand. I mean, a guy whose estimated rank is 30+/-20 is a lot different than a guy whose estimated rank is 15+/-5, but "level" treats them the same. Of course it's not going to be as good a predictor as, say, mean skill.
Re: arbitrary cutoffs
There is this notion of "consistency" in estimators: you have some parameter t you want to predict, and you have some set of n observations that you want to predict it from. You generally want the following: as n increases, your estimate gets closer to t. Dropping relatively recent observations from the past from consideration guarantees that your estimators will not be consistent. This is a pretty bad thing, considering that you don't really get any offsetting benefit from it.
Re: decaying the past
There are two things going on here, which it seems some posters are missing. Suppose first that skill levels are fixed, like people never improve or get worse, and our goal is correctly assess everyone's skill level in an asymptotically consistent sense. Then we should not drop anything from the past, and all observations should be equally weighted. Then the probably is basically simple except for what prior beliefs we have about the population of isotropic players.
Okay, but not skill levels aren't fixed, so we have to do something else. The Glicko solution is basically to increase the variance of the prior on each player over time. This naturally decays the impact of older games. This is the "gamma" that rspeer mentioned, as far as I can tell. Now applying this solution, but only on days you play, has a totally counter-intuitive effect on rankings. Consider two guys A and B, who on day 0 have identical mu/sigma rankings. Then A goes to study for the bar exam, while B plays a game a day for the next two months, during which time his results are right in line with his previous ranking. This system will claim, obviously implausibly, that we are MORE uncertain about B's ranking than A's, which doesn't make any sense at all.
Now, rspeer mentioned a problem about players playing badly at first and not being able to dig themselves out of the hole fast enough. To my mind, this isn't a problem: our best estimate of their level is what it is under the parameters of the model, so meh. But I think his comment reflects a prior belief about the distribution of skill levels that is a) not accounted for in the model, b) probably true. That belief is that the rate of change of "true" skill levels is much higher for players with low rankings than it is for players with high rankings. To me this is obviously true; when you suck, it's easy to become marginally competent, just read dominionstrategy.com. When you are mediocre, it is harder but not impossible to become strong. When you are strong, it is difficult to become elite OR to become mediocre. When you are elite, it's hard to move anywhere. The higher your meanskill ranking is, the lower the variance of the drift of your meanskill, regardless of the variance of your meanskill.
So if this is really the problem you are trying to solve with all this tweaking of the system, then just use non-uniform gamma based on meanskill. Problem solved, and in a nice Bayesian way.