Get yourself a decent pressure gauge and check your tires regularly, they lose pressure over time. A decent pressure gauge can't be beaten for accuracy, but if you're on a budget by the simplest. Oh, and never trust the petrol station pressure gauge's, it they even have one. It is not uncommon that a Thai boy does the tire pressure on good luck, as no pressure gauge is available.
Correct inflation is very important. Tires are remarkable things designed to cope with all kinds of abuse, but to maximize the grip they need inflating to the tire manufacturer's recommended pressure. If you've got a memory like sieve, scribble the magic numbers on a scrap of paper and keep them in your wallet.
Track pressures differ to road pressures and you need to adjust them accordingly. Generally, that means lower.
Take advice from the tire manufacturer for a recommended pressure, but be aware that it gets more complicated depending on the tire you're using, the weather and even circuit. You can also take advice from your tire fitter, or your track-day organizer who'll have some form of tire facility. As a rule of thumb, and only as a rule of thumb, it should be around 32psi front and rear when cold. The front tire starts with more air than when cold. The front tire starts with more air than the rear because it doesn't work as hard as the rear and doesn't warm up so much in use. Think about the relative work the front and rear tires do, and it'll make sense.
There's a strong chance your tires are incorrectly inflated right now. The loss of pressure can be subtle and hard to notice. Not enough air in the front means it'll turn more slowly. A good tire fitter should provide you with new tires correctly inflated, but never trust them. Check the pressures after your tires are fitted, with your own pressure gauge, for your peace of mind if nothing else.
Over-inflated tires will do the opposite of an under-inflated tire. Basically, the carcass and sidewall won't deform enough as you hit bumps, corner and brake, reducing the size of the contact patch and, ultimately, grip.
Be honest. How much time do you spend on the road? Almost all your riding maybe? Track-biased tires are less stable on the road, will warm up slower and have less tread pattern designed to disperse water. Road tires, on the other hand, don't offer the same grip on a track and are more likely to overheat. Use the best tires you can for the riding that you do. Tire manufacturers aren't stupid. If they say a tire has been designed for the road, that's what it will do best. Track tires rarely get up to working temperatures on the road, so the road anyway, so the idea that you're getting 'more grip' by using a track tire on the road is not true.