Do you mind if…和Would you mind if…在意思上没什么区别，只是后者在语气上更客气些，更委婉些。我的理解是，在Would you mind if…中，if从句通常（不是一定）用一般过去时。如：

Would you mind if I sat here?

Would you mind if I taped this conversation?

Would you mind if people smoked in your house?

Would you mind if I asked you to do something?

Would you mind if I brought a friend to the party?

但是不是说Would you mind if…的从句中用一般现在时就一定是错的呢？这也不一定，比如Cambridge Advanced Learner's Dictionary (2nd edition published 2005)就认为Would you mind if…的从句中用一般现在时和一般过去时都可以，该词典给出的例句是：

Would you mind if I open / opened (= Can I open) the window?