Are there any problems opening a helipad close to an airport?
In the US, normally it is not a problem.  I would talk with the tower supervisor, to see if a planner could be consulted before you go too far down the road and start paving or something like that.

A good place to start would be a memorandum of understanding, where you and the FAA would work out the operations out of the field, and discuss arrival and departure coordination. 

I could come up with a list of twenty heliports within 1.5 miles of Class C or D airports. Funny how hospitals end up near airports. Ditto for police facilities.

Life is easier if you do not plan on trying to get instrument approaches.