Is it true that the first thing women check out on a guy are his glutes?

Well, you're close. It's not the shape of a man's ass, but whether or not he is one.

As an anecdotal datapoint a long time ago I used to work in market research and we used an eye tracking machine and software to measure peoples unconscious eye movements when confronted with store displays and the like. Both women and men looking at a man would invariably create a straight line from face to crotch and back again repeatedly for the first few seconds. Both men and women looking at a woman would create a diamond shape on our screen with the corners of the diamond exactly where you'd guess they'd go. The effect was so uniform that we used it to calibrate the machine.

Well defined glutes are indicative of strong muscles meaning a greater muscle control, thus greater ability to contain explosive diarrhea. When looking at the world through this metric, I would assume that, yes, heterosexual women would want a man capable of controlling explosive diarrhea as this leads to less poop exposure. Otherwise, no.

I recently heard that - after such things as the face - the one thing women check out first on a male are his glutes. If the woman is checking out the face first, she's necessarily not looking at the backside first, right? For some science that may or may not be relevant to you, http://www.ojr.org/ojr/stories/070312ruel/ is a study that examined where and for how long people focused on various images. Scroll down to the baseball player.

Women on scripted TV seem prone to checking out mens' butts. I suspect it's because it lets them be sexual but not as crude as if they were checking out their package. It's a little naughty but not too naughty.

I can't really speak for womankind in general, but your proposition sounds logistically problematic.

I always x-ray my man to assess the size of his left ventricle. I'll settle for nothing less than 7 cm diastolic.

No. Sorry if you've been knocking yourself out on the Stairmaster.

No! In general, any claim such as "all women like x" will be false, because any claim of the form "all people of a certain type have the same characteristic x" will be false.