You might want to get a Home Inspection performed by an ASHI-Approved Home Inspector, where your inspector, himself, is acute to 'spotting the visual contributors' to water in the crawl (and/or basement.) Ask the Inspector what is 'crudentials' are with regards to this. (My Inspector was a Structural Engineer and his partner was a former General Contractor. They'd been in business 17 years doing home inspections when I 'found' them.) This is $$$ well spent especially when you may end up paying who-knows-how-much $$$ to fix the problem. The Inspector should be able to tell if the water was/is making a 'repeat showing' or if it's the 1st time (or so) that it's appeared. Hopefully, there's access to the crawl. Tell the Inspector the length and width AND heighth of the crawl and ask if he'll go inside it. He may not, either because it's too small or he just doesn't do it. Maybe they charge a separate 'fee' to go in. (Usually it's 'visually inspected' with a flashlight through an access-way.) Do tell them 'how' one would get 'in' the crawl too.
The 'things' that contribute to the water may vary. They include, and are not limited to the following:
Leaking gutters, incorrectly hung gutters, no gutters, no downspouts, inadequate sloping AWAY from the foundation, negative sloping towards the foundation, missing/no downspout extensions, underground spring, high water table.
Yes, you should be 'concerned' about this. In fact, I usually recommend that prospective home buyers pre-plan a visit to a home they're interested in immediately after it rains (for this type of reason.) As for the consequences of moisture in the basement, yes, there can be. They include, and are not limited to, the following:
rotting wooden joists, potential breathing problems for those people with 'sensitive lungs', mold, mildew, 'strange odors', high humidity levels, damp & ineffective insulation, buckling floors, termites.
A routine home inspection is in order and HOPEFULLY your Agreement of Sale has a provision for this. If not, I don't know what to say. In this light, you SHOULD have a Real Estate Attorney over-looking your 'interests'. They, too like the Home Inspector, are necessary, IMO. Otherwise, who else is looking after YOUR interests??! (Plez don't tell me that the Seller's Realtor is looking after your interest. They can't because, well, it's a conflict. They're being paid by the Seller.)
If you're looking at the prospect of paying 100's of 1000's of dollars in mortgage payments, spend a few 100 $'s on good Home & Legal advice by getting yourself a Home Inspector and Real Estate Attorney. Otherwise, you may end up having to hire an Attorney after-the-fact. (At least now, you don't have to pay any 'retainer', and after-the-fact, they're already 'retained'.) And your ASHI Home Inspector will usually return to your home in the event you 'discover' something you don't like after Closing. I could go on and on but I think you get the picture. If you have more ?'s, post up or e-mail me directly.