It depends on what you're looking at. If you're on a PC and are outputting in 1080i, you will see a slightly blurry picture compared to 1080p. I personally hate interlacing. I'd rather drop down to 720p than put up with an interlaced picture.
You have to see images of 1080i versus 1080p in motion to really see the difference.
It depends on the source. If it's an HD DVD or Blu Ray then you can have a display or the drive deinterlace it, no difference unless the TV's deinterlacer sucks.
The "no difference" line depends on a lot of things.
Is anyone still capturing video as interlaced video or is a progressive video capture simply being split into fields to match the 1080i broadcast standard? If the video is captured initially as interlaced, then there is most definetly a difference between 1080i and 1080p even after deinterlacing occurs. If the two 1080i fields are simply a single split frame of a progressive capture AND the TV deinterlaces properly THEN there would be no difference between 1080i and 1080p after deinterlacing.