You can scale in the Sequence AND/OR on output.
I'd have to run tests to see if there's a difference. There is in Ae. It's better to scale in a Comp in Ae over the Output Module. If you have a CUDA card, I'm guessing that scaling in a Sequence would be superior, as that's one of the purported benefits of the card.
We might need somebody like Todd to confirm this.
I scale in the Sequence all the time, and get great results. I export the Sequence size for mastering, and scale down for review movies.
Why do you say "mistakenly?" If you shoot 1080 and edit 720, you scale down (66.666%) to fit the full 1080 into the 720 comp. If you bring your 1080 in at 100% scaling (actual size - default scale to frame size pref unchecked), that gives you the effect of scaling up in your 720 comp, but with no loss of resolution.
Let's see if I can confuse the situation any ;-)
You have a piece of paper on the table in front of you. There is a rectangular hole cut in the middle, let's call it "1280x720" (compare to the viewable area of the Program Monitor in a 720p sequence.) You have a photograph, which is 1920x1080, under the paper (your 1080 video clip). It is obviously larger than the hole you are viewing it through, so you can only see 66% of the photo through your window. Looking through the 720p window and seeing only a portion of the larger photo, you have in effect "zoomed in" but without ANY quality loss - No magnification going on!
The 1920 image will fill the screen if you scale DOWN to 66%, or you can go up to 100% and see a portion of the image, without any upscaling/quality loss. If you scale beyond 100%, then you are blowing up pixels and the more you zoom in beyond that, the more degradation. Keyframes can of course be used to animate scale and position anywhere in that 66-100% range with clear results.
As you can imagine, if you put that 1920x1080 clip into a 720x480 SD project, you could really zoom in much farther without loss!
Just make sure to right-click your clip in the sequence and verify that "Scale to Frame Size" is NOT checked before beginning. You should be seeing the middle of your clip only and not the entire clip.
Hope this is clear now. If you start with a 1080 clip in a 1080 sequence and zoom over 100%, that degradation is already there then, and will carry over to whatever format you export to, whether 720p, or SD, or whatever. You don't get the resolution back, unless you edit IN the smaller sequence format as described above.
Safe Harbor Computers
I said "mistakenly" because I was scaling in a 1920x1080 sequence and outputting my final version as 1280x720 not realizing I was losing resolution. I would like to thank everyone for helping me get a better understanding of how premiere handles the scaling.
Jeff thank you for the excellent example. I just output some footage using your method with no loss.