Solche Probleme hatte ich auch gelegentlich, ich weiß jedoch nicht ob dies auch beim Opera-Browser war.

Meine Lösung war da recht simpel:
Statt die Adresse im Format 123.456.789.012 einzugeben 'http://' davor packen, also im Beispiel wäre dies dann http://123.456.789.012

I narrowed down the problem by myself by now.

Somehow it was some kind of weird interaction of an extension with the updated flash plugin. Weird because click to play seemed to work with all sites but one (and especially one with lots of embedded flash videos) after the flash update.

The extension that seemed to cause it was "Site-specific Preferences". From one day to the other (exactly the day that NPAPI plugin stopped working) the Operas click to play setting for all pages was overridden by the site specific extension settings from "Ask" to "Allow". Setting back the status within the extension to "Ask" for this specific site solved the problem.

Just found another issue with the PPAPI plugin:
For whatever reason the "click to play"-setting doesn't work anymore. Which is really bad on an underpowered system.
Is this behavior normal with PPAPI? Or is this something that might be caused by using the debugging version of the plugin (again, the installer for the regular plugin crashes on my setup)?

That's too bad. Because when testing a couple of things to get Flash running again, indeed I already tried to install the PPAPI plugin via the preferences pane of the Flash plugin (which just redirects to https://get3.adobe.com/de/flashplayer/update/ppapiosx/). But Adobe's PPAPI installer always crashes on my system.

Excerpt from the crash log:

Exception Type:  EXC_BAD_ACCESS (SIGBUS)
Exception Codes: KERN_PROTECTION_FAILURE at 0x0000000000000000

VM Regions Near 0:
--> __PAGEZERO             0000000000000000-0000000000001000 [    4K] ---/--- SM=NUL  /Volumes/VOLUME/Install Adobe Flash     Player.app/Contents/MacOS/Install Adobe Flash Player
VM_ALLOCATE            0000000000001000-00000000000d2000 [  836K] ---/--- SM=NUL  

Application Specific Information:
objc[9133]: garbage collection is OFF

Thanks for the help.

OK, I finally got Flash working again when installing the PPAPI-plugin "Flash Player content debugger for Opera and Chromium based applications – PPAPI" from https://www.adobe.com/support/flashplayer/downloads.html

The recommended installer for PPAPI doesn't work on my system (it always crashes), so I hope the debugger plugin doesn't have any downsides for normal users.

I'm using Opera 29.0.1795.60 on an older MacBook running OS X 10.75. Almost from one day to the other suddenly Adobes Flash plugin stopped working. Opera tells me, that Flash is outdated and that I should update it, despite that I'm already running the most recent version.

Here is a screenshot of opera running the Flash Player Version site (http://www.adobe.com/software/flash/about/) with the mentioned error message (german localization):
http://i.imgur.com/XCOYpPz.png

Same results with Youtube, of course:
http://i.imgur.com/3GT1ZkN.png

I'm already tried running the flash update again, without any results. And btw. other Browsers like Safari and Firefox still work fine.

Well, the current problems with Flash v13 is not an Opera issue.
Adobe messed up... badly.
http://forums.adobe.com/message/6282551

V13 seems to work on most OSX 10.9 Mavericks Systems without problems. But it looks like Adobe didn't test v13 with older OSX versions well.
So on many pre-Mavericks systems after upgrading to Flash v13 the Flash-plugin is broken with all browsers.
This happened to me as well, after trying to upgrade to v13 on a Lion installation and I'm not bothering trying the same on my other computer, that still runss with 10.6.8.

Adobe's solution?
Uninstalling v13 and going back to v12
http://forums.adobe.com/message/6285851#6285851

The same issue happened last year, and it took Adobe months to release a Flash version that worked with my older system.
It took so long that even Safari rejected the outdated Flash-version for security reasons.

The terribly annoying lag now last at around 30sec with Opera 12.16 (Mac)! And it's even worse with a slower computer!
So using YT now is something like this:
Searching for something - results are viewed -> for ~20-30 sec Opera freezes completely
Finally clicking on a video - video is loaded -> again Opera freezes for said time.

So it pretty much takes more than 1-2 minutes for viewing just a single video, which is pathetic and renders YT unusable.

And yes, this problem was caused by the new YT-layout. And the duration of the Opera freeze seem to depend heavily on the number of subscriptions etc. you are having with your YT-Account.
The main culprit seemed to be the new sidebar with it's subscription container. There even was a nice workaround found some while ago:
https://forums.opera.com/topic/858/terrible-youtube-lag-opera-12-16

Too bad, turning off the subscription container via User-CSS doesn't work anymore. Despite blocking that problematic YouTube-Element I now get the freezes again after a short period of getting Yt to work. So maybe the changed the layout again making it pretty much unusable with Opera 12.16

I made a small oneliner to count all the folders and urls inside the bookmarks.adr from the terminal (shell/bash):

awk '/\#FOLDER/ {folder++} /\#URL/ {url++} BEGIN {folder=0; url=0} END {print("Folders: " folder "\nURLs: " url)}' bookmarks.adr

Of course 'bookmarks.adr' needs to be replaced with the path to where the file resides. On a Mac for the active user account it can be found here:
~/Library/Opera/bookmarks.adr

Result:
Folders: 835
URLs: 6408

And the file itself is now 1.9 MB big.

And what I noticed on two macs with synced bookmarks via opera Link:
The Mac version of Opera 12.16 doesn't handle huge bookmark lists that well. When starting Opera from another user account that hasn't such a massive bookmark list, Opera "feels" much faster and responsive. Especially the problem of the Mac Version, that typing in forms (like now) or the address bar is slow as molasses, seems to be triggered by the bookmarks.

When starting Opera on both macs it takes some time (sometimes > 1 minute) until the bookmark list from the menu is complete. And typing something in the address bar, a form or even using a simple keyboard shortcut like CMD+C takes some seconds (worst case > 10 sec) until the browser becomes responsive again. What is weird, that when copying via menu instead of the shortcut there's no waiting time at all. But that mostly happens once after starting the browser, or sometimes for some reasons after longer times of inactivity. But for whatever reason copying texts via shortcut leads to a few seconds of unresponsiveness more often.