There seems to be a really easy fix for this, at least it fixed it for me.
Originally I had the same issues everyone else has had with not being able to adjust the height of the camera when using the tripod. I noticed though that in the PhotoCamera.ini file (the one located at \wherever your base games files are\Game\Bin_LE\res) that at the very bottom of the text in the file, third to last line, is a setting called "TripodUseFreeCam".
I kid you not, all I did was change the value there to 1 and after that I was able to use Q and E again when taking pictures with the tripod camera. I had the previous version (1.69.59) when I did this and I currently have the most current patch, and it still works just fine.
You can edit the file with any standard text editor, like notepad or notepad++ and just save it. I used Notepad++ so I didn't have to worry about checking to be sure it remained an .ini file when I hit save, so if you're worried just do Save As and check that the file type is still .ini before you hit save.
I did this for the PhotoCamera.ini file in both the Bin and Bin_LE folders, but if you have the 64-bit version installed you can just modify the PhotoCamera.ini file in the Bin folder. That was all I did to get the buttons to work again.
I recommend deleting the cache files and a few others that could cause issues afterwards. It's good to do this from time to time anyways, I do it every time I close the game.
To do this, go into the Documents\Electronic Arts\The Sims 4 folder and delete the Config.log file, the localthumbcache.package file, and any other log files or files with "exception" in the filename.
Also delete the spotlight_en-us.package file (depending on your language, the filename will vary slightly) inside the cachestr folder, but leave the cachestr folder.
If you also have the cache folder, delete the files in there as well, but leave the folder.
Delete the entire onlinethumbnailcache folder (not related, but never hurts to delete it to refresh things).
Beyond the exception files, the game will generate a fresh copy of all of the other files you deleted upon starting.
Some users are having issues with the A and D button functionalities inverting only while using the tripod and the bottom slider may not work, but you can replicate that functionality using WASD to move around and the mouse to direct the view. I'm not sure why it's causing that, but I'm working on figuring out the issue and I will hopefully find out the problem soon. The issue may possibly persist in the Flash Studio, but if you have Ksuihuh's AEP mod (adult film star career mod), you can choose (as the photographer) take erotic photo option on the flash studio and it will function exactly like the fixed tripod does. Or you can manually set up a photo studio with the separate components from build mode (you'll probably need to use the cheat bb.showhiddenobjects to see them).
I really hope that this fixes it for anyone else who has had issues with using the tripod.
EDIT by crinrict: Added solution banner for info