For example, this week I saw a video of a beheading. Now after watching it I probably wish that somebody had filtered that for me.
If it makes you feel any better, unless you watched a completely different video than I did (something other the what has been in the news recently), you didn't see a beheading. Did you see the blood spurt/drain out as the carotid/jugular were severed? Did you see the disarticulation of the spine? Those weren't in any version of the video I saw. It moves from a guy making a sawing motion with a knife in front of a guy throat, to a picture of the disembodied head sitting atop the body.
That's not to say that the guy is any less dead, or that it was any less horrific. But there was a lot of somewhat creative editing going on in that video. Shadows seem to shift at different points relative to the background, indicating that some of the later parts may have been recorded an hour or two after the earlier parts. There is some analysis that seems to indicate the "terrorist" may have been two different people at different points in the video. There are a lot of cuts, and quite a bit you don't see.
I'm not saying the video is a complete fake. The guy obviously suffered a horrific death, and the perpetrators need the full weight of the western worlds power brought down upon them. But don't beat yourself up about watching a beheading -- what was shown was both sad and shocking, but it left out the actual beheading part (again, unless there is some special uncut version out there I haven't heard about).