If the tank is close to empty, you'll smell the gas odorizer more than with a full tank. Otherwise, to test the fittings, get a spray bottle with some liquid dish soap and water and spray the fittings. If they are leaking, they will foam.
I just filled my 'spare' propane tank today- I rotate between 2 of them- and saw a sign at the propane store that after 11 years, tanks have to be re-certified, then each 5 hereafter. If your tank came with the grill, it might be reaching the end of it's time.
Incidentally, I think those 'Blue Rhino' or other pre-filled, exchange tanks at home centers or convenience stores are a rip-off. Better to buy an empty tank at Costco ($20+-) and have it filled at a propane dealer ($15ish).
Jim Ricks