Should I mention in my letter of recommendation that my student has bad handwritting?
I would not mention this no, this should not have any consequence to the students application, it may be a little out of place. It would be worth advising the student to inform any future places of study about his handwriting he may be able to get some alternate support with regard to exams. 

I would not see this student as a liability, just maybe needing a little extra support in this area, it is fair for an examiner to not spend ages marking one students paper due to bad handwriting, so long as they give it a fair go and a good effort.