Jarmo9, @all,
I can confirm what happens to you by 100%. I'm using two devices, a iPhone 4S, 64GB and a iPad 4, 128GB. I'm a "heavy user", meaning I had more than 1600 Apps on each device. After upgrading to 7.1 BOTH devices started to reboot continuously. The upgrade was done via iTunes on the iPAd and over the air on the iPad.
The first action was of course, to restore the lastest backup. In DFU mode. But during the restore, both devices started to reboot in a loop again. The reboot loop starts after restoring approx. 1400 apps. The logs shows SpringBoard, EXC_BAD_ACCESS, KERN_INVALID_ADDRESS and Watchdog timeouts with Exception Code 0xfaded321 or As well Reset Counter logs.
It's worth to mention, that the device is not starting from scratch again within the reboot loop. Althought it always shows the white apple logo on the black background, the restore process continued in iTunes after a short pause.
Amazingly the log entries matched on both devices, so it's definitly not a device memory issue.
Next action was to setup both devices new. But gues what append on the iPad after installing approx. 1400 apps MANUALLY: The reboots started again. I experienced exactly the details what you wrote: The screencapture doesn't work. Secondly: Since I'm using a complex PW with letters, I need to use the iPad keyboard, which doesn't show all characters most times. Instead there are empty placeholders / boxes.
I really look forward that apple will urgently release the next iOS Version, which hopfully will fix the reboot horror. In the meantime I'm using only 50% of the 128GB memory, which results in hourly reboots. Same for the iPhone, which is running pretty stable with 30B free memory.
I observed something interessting: After changing the language from German to english (or vs. versa), the screencapture is working for a limited time and the device overall seems to be more stable. However, there is definitly a memory but in iOS 7.1. Of course I visited the Genius Bar, which was to much for them. They even were not interessted in dumps or ticket details, opened upfront via Phone. The first advice was to reset the device via the DFU mode, which I had done 10 times or more on both devices. I declined this, and asked if they are able to interpret the logs or to do something else. What a ridiculous conversation, they even did not open the logs are start a memory test.
The best joke was, that the store manager in Frankfurt / MTZ offered me to buy a new iPad device, since there is no way back to iOS 7.06, which I asked to install (beeing aware that this is not possible or let's they forbidden ...) I personally did accept this by signing apples terms and conditions. ah.. After the store manager switched the communication to this level, I stopped. Obvisously the retail team is not empowered to do more, they even won't or can't open a complain. Sad, Sad
Thanks to apple for advising me to their Terms and Conditions. It's really anying that apple ruins working devices by submitting a new Firmware / Software with NO WAY BACK. Even after opeining a ticket and visiting the Genius Bar with a reproducable scenario.