It's very easy to find hot pixels by shooting anything in total darkness. You can add a second check by doing the same thing on a white surface -- I wouldn't blow out the image though.
For video, "hot pixels" are what you want to avoid because they show up rather distinctly on videos, especially in a dark environment. The very first video I shot on my 5D3 showed a red hot pixel in the lower half of the screen, and I only had the camera for about a week at that point. Fortunately, you can fix it rather easily...
1) Remove the lens and place the cap on the camera
2) In the menu functions find the Sensor Cleaning menu
3) Select "Clean Manually"
4) Let it sit for 30 seconds and then switch the camera off
5) When you power back on all pixels should be remapped
This apparently works on my of the newer Canon DSLRs, but I can definitely vouch for it successfully fixing a hot pixel on my 5D3.