Another place that (rain) water can get into the hull is anywhere you have something screwed into the floor, console,Fuel tank retaining straps. If the sealing around the screws has broken down you would be amazed how much water can ingress.
And yes it will seriously affect the handling!
Another place is if you have an anchor locker that drains into the hull then obviously, the more time you put wet rope into the locker , the more water gets into the hull.
We always have good quality stainless steel bungs fitted to our boats. Our boats are generally lifted and drained each evening. I would not be surprised that even with good bungs that a boat left afloat for weeks at a time would take some water into the hull !
Hope this is of help!