We had the same errors on one of our installations after upgrading to 5.6.1. Then the Action menu problem rang a bell. In DNN 5.1.1, the blog module had an error and you had to modify your container skin to allow the blog menu to work. Many of us inserted additional parameters to the container skin as instructed below:

http://www.dotnetnuke.com/Resources/Forums/tabid/795/forumid/92/postid/361020/scope/posts/Default.aspx#361020

So now, since the blog module has been fixed of the edit menu problem(s), we modified the container skin and removed all the extra parameters in the skin, save them and then turned compression back on.

No errors! We also found that the Media module had a problem and as soon as we upgraded it, that error went away as well.

Hope this is the reason for most everyone's errors on 5.6.1 with compression.

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