Hello, I had a 96 taurus with the same problem. When you pulled the hood release you would then need a screwdriver to pry the hood open farther in order to get your hands under there to pull the safety release. Either the hood release has too much slack or a spring is not doing its job. BTW I never bothered to fix mine I just lived with it. GOOD LUCK!
I would def. try shoz123s sugg. first. Easiest and good preventive maintenance. First, spray latch (top and bottom) with pb blaster or wd40 to clean it up, and secondly, spray it with some white lithium grease for lasting protection. Paul (shoz123) is very knowledgeable and his advice is right on!
I agree that the latch can easily be the problem, I had to lube it too to get it to release properly. However that's not all the solution I needed since the hood struts/lifts are another outstanding problem at least for me, they barely extends on their own and I will have to literally pull the hood open all the way to the top. It then barely hold the hood in the up position and will slam close at the lightest wind blowing against it. I've gotten my head knocked by the hood several times until I replaced them, now they pop up, extend, and stay up correctly that I replaced them. If you don't believe me you can push against your old and new units outside of the car, against the floor. and you will find the old ones much easier to compress like that of a old suspension strut. a new one takes a lot more force to compress.