Singular third person "they" is widely attested and there is no grammatical problem with it at all. It's even in Shakespeare. You can use it, and if anyone complains about it, don't hire them.
Also, citation needed for using 'they' as singular. Apart from the fact that it very strongly sounds plural, one of my personal pet peeves with English is the fact that we do not have a singular plural differentiation in the second person. As long as we are re-working pronouns, lets not repeat that mistake.
When I am trying to be careful and gender neutral (for something that needs to be speakable, so no (s)he), I try to structure it to use either 'one' or 'that person' in place of (s)he.
Seems to be an artifact of older formally trained english teachers.
http://english.stackexchange.com/questions/30455/is-using-he...
Using "he" has fallen out of fashion.
Call me a purist though, but I still detest using "they". It doesn't seem right.
http://languagelog.ldc.upenn.edu/nll/?cat=27
and approval here:
http://www.justice.gc.ca/eng/dept-min/pub/legis/n41.html
For the plural second person, try out my ancestral dialect's "y'all".