And for a completely alternative, alternative point of view ... (thus began the next round in the never ending yeast storage and propagation debate)
I wouldn't store liquid yeast for too long in any case - if you want long term (more than 1-2 months) storage you need to get into slants.
I've stored it for up to 6 months before and it has been ok. Basically as long as you take into account the loss of viability at that time and pitch more to compensate it is ok, and you can definitely use it to make a starter from, especially if you wash it first to get the viable yeast up in to suspension.
Also different yeasts behave differently and can be survive for different lengths of time. I have found it very hard to slant and/or store Wyeast 3068 for any length of time, where as 1098 I have stored for 6 months with no discernible problems that is you can not generalise when it comes to the different yeast strains.
That said, these days I slant all the yeast that I store long term.
For liquid yeast, my advice is don't mess with it; you just risk damaging it every time you do. Under a low alcohol beer is fine. Well within the yeast's tolerance and the trub and wort provide a food source for the ongoing (though slow) yeast metabolism.
Washing refers to cleaning the solids - removing the hops and trub from the yeast. I don't think it's worth it as it's a lot of mucking around for little advantage. The hops have no benefits for yeast storage, they don't "preserve" the yeast.
Again I beg to differ. You want to ensure that you pitch strong health vigorous yeast cultures. To do this you need:
i) Ensure that the yeast you start with is still true to the strain that you want to be propagating (ie not recultured from a 12 month old bottle or dregs, or one that has been used too many times and hence had plenty of opportunities to mutate). I think it goes without saying that you should never reuse yeast that there is any suspicion in regards to infection issues, and you need to be double cautious with sanitation practices when storing and propagation yeast.
ii) Ensure that you have healthy viable yeast by either doing an appropriate sized starter, using low gravity wort (~1.030) at 22-26C with some sort of nutrient. ie give the yeast every opportunity to be fighting fit before you pitch it.
iii) If you are repitching from a previous fermentation make sure that you do not leave it too long ( > 2-3 weeks depending on the strain ), and that you don't reuse it too many times (especially if the yeast is been worked hard with a high gravity beer ).
I have tried many ways of re-using and propagating yeast and most of them work after a fashion, with some working better than others and being very dependent on the actual strain you are working with. It does not matter so much how you get the yeast to propagate ( ie slant/wash from a previous cake/culture from a commercial bottle), as long as you are sure the strain is relatively pure, there is enough viable yeast to inoculate the wort (before the bacteria does) and the yeast is clean you should be able to propagate it.