But my question is...will a knit AND purl stitch look the same on the needles? I know the leading edge of it should be in the front and slanted towards your left thumb.
I don't relate to your description of the stitch mount. The way I think of it is that as the loop is sitting on the left needle, the leg of the stitch nearest my body should also be nearest to the tip of the knitting needle. This is true of a knit or a purl stitch.
What happens to your work if you miss a twisted stitch and just knit it and continue on...
If the stitch is a purl stitch and it is not sitting correctly on the left needle before it is worked, it will look fine once it is purled onto the right hand needle. So if you were working a sweater and the purl was on the outside it would be fine because the resulting knit stitch on the inside wouldn't show. But since you are working a blanket and both sides will show that is not as nice.
If you purl a stitch and weren't sure it was mounted correctly before you purled it, you can turn the work immediately and look at the resulting knit stitch just below the needle (it will be the stitch below where the yarn is attached), the bottom of that little \ / should look like that with a bit of an opening at the bottom, but if the purl was backwards the bottom of the vee will be closed and actually cross over itself. If it does, turn back to the side you were working on, tink the stitch and then change the mount and purl again, check it again to make sure it is right.
If it is a knit stitch that was mounted incorrectly, as soon as you work it, without turning, the stitch right below the right needle will be crossed at the bottom instead of being open. Do it over.
By careful observation and a little experimenting you will soon be able to prevent twists. Also in case you didn't know, if a knit stitch is sitting on the left needle wrong you don't have to turn it around, just knit it behind the right needle instead of in front and it will straighten out. Presto! (the knit feels a bit like a purl because you enter the stitch with the two needle tips pointing toward each other).
Same is true for a purl but to purl through the back loop feels a bit more awkward. With your yarn in front (cause it's a purl) and working from behind the left needle, run your right needle starting to the left of the stitch loop, into the stitch so that the needle sticks out in front of the left needle between the two legs of the stitch, from there do your yarn around and purl the stitch. This will straighten it out.
That is a detailed description. But hopefully it makes sense. It's not hard.