Is it ok to mix 23 and 25 tyres My road bike comes with 25 tires. They both seem to be slick smooth ones with little resistance.    Recently I had couple of punctures in the rear and I decided to change the rear tire to a 23 which was more puncture resistant and better grip.    

Is there a problem in using 23 in the rear and 25 in the front?
There isn't a problem with it, though you may find your ride quality to go down a bit by moving to a smaller tire (but 23 and 25's don't really have much cushion to begin with so this won't matter too much). There is also a slight change in gearing due to the change in diameter of the tire. Generally though, I'd expect a bigger tire in the rear than in the front due to where you sit. 

In general, you can mix tires so long as they go on the rims and clear the frame + brakes. Here is everything you want to know about tire sizing, including recommended rim widths for given tire widths.