Yes, there are very few reasons for not applying to multiple law schools. By applying to more than one school you, obviously, increase your chances of getting into a school you want to attend. Even if you know which law school you want to attend, and are heavily relying on attending that school, there is a chance you may not get accepted to that school; it may not be based on your qualifications but the school's seats may all be filled etc. Thererfore, you should have a plan just in case the school you wish to attend does not, or can not, accept you for some reason. In addition your circumstances may change and you may decide the law school you chose at first is not a good fit for you given your new circumstances. If you feel that your undergraduate GPA and your LSAT score(s) are not up to par then you may want to increase your chances of getting into a better law school by applying to multiple law schools. Also, if you wish to attend a state school to save money on tuition versus a private school you should apply to many state schools because if you are not a resident of the state there is less of a chance for you to be admitted as most state schools reserve 75-80% of their seats for residents.

The adverse effects are that you may have to reveal what other law schools you are applying to on some law school applications which may possibly be looked negatively upon by the law school admissions board. However, this seems like a minor adverse effect. The obvious adverse consequences are that you will have to spend a good deal of time and money applying to other law schools. Law school application fees often cost $25-$65 per application and require other documentation (which requires fees to obtain) and can take a good amount of time to complete each application and supporting documents.