Solder question

[--M]

    I have a question about solder and cleaning rosin. I have been
soldering with .022 "Silver Bearing Solder" 62% tin 36% lead and 2%
silver. I like this solder it's very fine and solders nicely very clean
to work with. Everything I have done with this seems to work just fine.
Everybody seems to recomend rosin core solder. I got some of this and it
seems to work just as well but leaves rosin on the PCB when I am done. I
have never bothered to clean this off is there a potential problem here?
How would I go about cleaning this off, does it matter?

Thanks

--M