This last solution from jethro is clever and effective, but, with such a problem, I would rather take the solution offered by Corion. I think that, faced with a problem like that, it is often better to think is terms of several simple regexes checking individual conditions, rather than building a single more complicated regex to match all cases. Assuming I have to read and understand some undocumented code, I certainly prefer to have something like:
do_something() if /\d/ and /[A-Za-z]/;
which tells me immediately that I need at least one letter and one digit, rather than:
do_something() if /\d[a-zA-Z]|[a-zA-Z]\d/;
which is quite clear in term of what it does, but less obvious in terms of what the intended underlying rule should really be. Having said that, I also sometimes use these types of supposedly clever shortcuts when they save some typing. But that often implies that I need to add a comment to explain the whole shebang, meaning that I don't save so much typing after all.