From Mr. Malty:
"If you've brewed more than one batch, I'm sure you've noticed that there is a huge pile of yeast in the fermenter at the end. If (and that is a big 'if') you've got excellent sanitation all the way through the process and have provided proper yeast nutrition (including O2), you have a gold mine of healthy yeast ready to reuse. Of course, you don't want to reuse the whole thing. I know a number of people dump a new batch on top of the yeast cake, but you're not going to get the best beer that way. Yeast do need some growth to result in the right kind of ester profile, etc. While too big a pitch is better than too little, it is pretty easy to figure out how much you need and pitch just that.
There are about 4.5 billion yeast cells in 1 milliliter of yeast solids (solids with no excess liquid). According to Fix, in a slurry, only about 25% of the mass is yeast solids. Of course, if there is a lot of trub in there, you have an even lower percentage of yeast solids. The bad thing is that you can't tell how viable that yeast is, unless you have the equipment to properly test and count it. So this is where it gets a little bit like black magic. There are a number of factors that affect the viability of a given pitch of yeast. How old is the yeast? How stressful was their last fermentation? Have they had the proper environment and nutrients for successful reproduction or are they too scarred and tired to go on?
When the yeast is fresh and healthy off an previous batch, viability is maybe around 90%+. It goes down from there fairly quickly without proper storage and it also really depends on the strain of yeast. Unless you're going to get into testing viability, you're going to need to make some educated guesses and keep good notes on the results. This is where being a yeast psychic really helps. Start in a range of 80 to 90% viability and you probably won't be too far off. Use the Pitching Rate CalculatorTM to help figure out how much of that yeast you need. If your yeast viability is much lower than 90%, you should probably toss the yeast. If you really want to use it, you might consider pitching it in some starter wort to get the still viable cells active. When they're in solution, decant that active part of the starter into another vessel, hopefully leaving the dead cells behind."
The pitching rate calculator Jamil speaks of is at www.mrmalty.com
You are not storing washed (i.e. "rinsed") yeast, you are storing slurry and can expect its life expectancy to be shorter accordingly. I think your best bet is to either rinse the yeast properly, or use half a cup or maybe a cup of your slurry in a new batch in the next week or two, then rinse the resulting cake from that batch accordingly.
Or, if you are worried, just toss it. Yeast is relatively cheap, especially dry.