I get the same behavior when I run your script under Yosemite 10.10.5
No change on this point, except perhaps your memory 
May you explain why you need to define this property his way ?
From my point of view clean coding would be :
property pathToMe : missing value
on run
set pathToMe to ((path to me) as text) --works as expected
display dialog pathToMe
display dialog (my forSee())
end run
on forSee()
set newPath to pathToMe
return newPath
end forSee
I would never rely on a code using path to me in the definition of a property.
My understanding is that at compile time your instruction define pathToMe as the path to the Editor. I repeat that it behaves this way in Yosemite too.
The alternate scheme :
property pathToMe : missing value
on run
set pathToMe to path to me
end run
defines it at first run so it grabs the correct path, even if you move the script on an other device.
As I wrote in an other thread I dislike storing a variable value in a property because it modify the file so GateKeeper is not satisfied. I would code this way :
script shared
property pathToMe : missing value
end script
on run
set pathToMe to ((path to me) as text) --works as expected
set shared's pathToMe to pathToMe
display dialog pathToMe
display dialog (my forSee())
end run
on forSee()
set newPath to shared's pathToMe
return newPath
end forSee
Nothing is changed in the file itself when we run it so there is no problem with GateKeeper.
Of course, the properties are not permanent but I see no reason to make the one listed in your original message permanent.
I must add something.
My own memory was wrong. When I run my code under Yosemite it returns, exactly as it do in El Capitan
“SSD 500:Users:me:Library:Autosave Information:Document Éditeur de script non enregistré.scpt”
The volume name changed because the OSes are on two different units.
Yvan KOENIG running Yosemite 10.10.5 in French (VALLAURIS, France) mercredi 30 septembre 2015 20:49:07