I just updated to Unity 5.1.2p3 and am running into… I can’t select a single mesh like I was able to do just an hour ago before I updated. I can only select entire groups via a window select or from the Hierarchy window.
Yes I am in a SCENE WINDOW.
Yes I’ve checked and the LAYERS are all unlocked.
I’ve closed and reopened Unity and it is still happening.
Very frustrating!!!
I can select an object from the hierarchy list, or by windowing over the entire object. I can still work, but it is frustrating when I have a ton of objects in a scene and I have to go find it in the hierarchy list to select it. I keep objects nested in groups to keep things organized, and now I have to go searching for ANY object. The crazy thing is, clicking on an object worked last week, but then when I reopened the project, it stopped working. This is only since I updated to the new patch. 
I’ve also had this exact problem after updating to 5.2.0f3. I was able to fix the problem by closing the Scene tab and adding a new one.
Hope this helps.
Have had the same issue here - I wasn’t sure if i’d hit the wrong button somewhere…
So I moved all files from “Project Settings” to see ‘what would happen’ -(Unity recreates them when it loads the prpject anyway) i lost all my baked maps etc but was then able to select objects again as normal.
May be that’s because you’ve locked all layers? You can check it in the Layers Drop-Down (Top-Right corner of the screen). If lock icon is ticked untick it.
I had this today, I had followed advice on a different post about locking a layer and hadn’t made the connection that this had caused the behaviour. To “fix” it I clicked on the layers dropdown and unticked the padlock by UI.