I put FCE 4 on a clean install Mountaind Lion and it appeared to work, see above thread.
Users find what you have already stated, ranging from working OK to not even being able to install.
Try it and see how you go. It's just not supported by Apple any longer with Lion or Mountain Lion.
FCP X is the new kid on the block that is supported.
it would be important to know what is the reality about FCE vs. Mountain Lion
The reality is that FCE was discontinued over 18 months ago, before Lion was even released. Apple does not support FCE on Lion or Mountain Lion. You are "on your own" if you use FCE on Lion or Mountain Lion.
Final Cut Pro X is the current application, fully supported on Lion and Mountain Lion.