My partial denture teeth seem short compared to my natural teeth. Will it cause any problems?

See dentist. Ask your dentist about it. Can also see the specialist - a prosthodontist - for an opinion.
See your dentist. This may can be repaired to make the heights more even. Perhaps there is a problem with the opposing teeth being longer.... Please see your dentist.
See a prosthodontist. If you are unsure if the partial dentures are right for your situation, ask your current dentist for a referral to see a prosthodontist. They are dentists specialist that have spent an additional 3-4 years specializing in replacing missing teeth.
See your dentist. The acrylic teeth can sometimes be replaced in as little as a day. If you've had your partial for a while, it may need to be re-lined, or you might simply need a new partial.
That is common . The partial denture teeth much sit in acrylicresin, which means that the gums are artificial around those teeth as compared to the natural gumline. This creates a shorter tooth in the partial denture. One solution is to butt partial denture teeth that are anterior replacement rather than wrap the acrylic resin into the lip vestibule. This makes them more likely to fracture, though.