I'm sure plenty of people have them.
Screen bleed is the most famous.
Randomly shutting off is common too.
HTC has crappy power buttons on a lot of devices.
I got bit by all 3 of those (but my power button wasn't quite dead yet) before I got bit by the bug that our flash chip has. I was trying to use my phone as a USB drive and copied a ton of stuff over, the progress bar stopped moving and the phone didn't seem to be running right, so I rebooted. Somehow it bricked and now the charging light wouldn't even come on. Started from the unbrick tricks, but I was way worse off than what they are for and near as I could tell something had disappeared really early on in the bootchain process and it was unfixable without direct access to the eMMC to rewrite the whole image.
Later found out once I got a pantech burst (which has very similar hardware) to replace my amaze that the MMC chip we have can get confused and randomly swaps blocks of storage around. It's easiest to trigger if you have lots of writes pending and the operating system tries to deallocate a block (like trim on a SSD); sometimes the chip will de-allocate the wrong block. Mine happened to garble something really close to the beginning resulting in my brick.
Much later I got a broken phone off ebay to rip apart to see if I could get the many gigs of data I MOVED to my phone immediately before it died only to find it just had a dead battery...maybe. It was well used, but didn't look physically damaged. It turned on but the screen was just static, like an analog tv with no channel. Couldn't get it working, but on other phones it looks like this is what happens when the chip in the LCD dies.
Combined the two broken phones to make a working one and find that this board has something going on where the battery drains when the phone is shut off, thus explaining why the battery that came with it was completely toast. Maybe I screwed up the rebuild, but I don't know how.
tl;dr: Yes, I have had some hardware problems.