This may be a template issue. I was not sure about what component to select. Anyway, this:

[b]test[quote="Tizius"]Quote 1[/quote][/b]

[i]test[quote="Tizius"]Quote 2[/quote][/i]

results in this:

testTizius:

Quote 1

As you see, the [ b ] BBCode is affecting the content of the quote (and I think it shouldn't, even if users should avoid putting BBCodes around quotes) and the [ i ] BBCode too. If you use subSilver2, the [ b ] BBCode works fine (i.e. has no effect on the content on the quote), but the [ i ] BBCode also affects the "title" of the quote. See the attached image to understand what I mean.

EDIT: Ahh! Ticket editing! Great!