I am still experiencing it. Granted I just tried out the new client just this moment so I could respond to your question with feedback so I don't know how bad it will be with prolonged use.
In the new client (13w17a) It will generate a new output-server.log file every time I open and close a world. However, unlike the previous client, it does delete 1 or 2 of the files when the game is closed but not all of them.
After loading and quitting my survival world a few times and then closing the game, I am left with the following files:
output-client.log
output-server.log
output-server.log.1
output-server.log.1.lck
output-server.log.2
output-server.log.lck
I am assuming all of those files were to be disposed of once the game was closed, correct?
So I would imagine that if I played like I normally do for hours at a time switching between test worlds that the folder would fill up pretty fast.
Had this happen to me earlier today but I assumed it was because I exited my world but left Minecraft running minimized all night. However, I often leave Minecraft running for days without problems so I'll comment.
Minecraft Crash Report ----
// Ouch. That hurt 😞
Time: 3/22/13 5:42 AM
Description: Ticking entity
java.lang.OutOfMemoryError: Java heap space
at dv.<init>(SourceFile:62)
at jc.l_(SourceFile:153)
at aab.a(SourceFile:1336)
at iz.a(SourceFile:508)
at aab.g(SourceFile:1314)
at aab.h(SourceFile:1221)
at iz.h(SourceFile:390)
at net.minecraft.server.MinecraftServer.r(SourceFile:462)
at net.minecraft.server.MinecraftServer.q(SourceFile:397)
at bjh.q(SourceFile:122)
at net.minecraft.server.MinecraftServer.run(SourceFile:331)
at gp.run(SourceFile:573)
Confirmed in 1.5.1, just tried it out on my flat world.
Having the same issue on 1.5, currently 71 files in total in my MC folder right now.
Well, I know my files came from the new client. I deleted them all before running the new one and watched the files get generated as I loaded / closed worlds and then closed the client. Then I deleted them again and went through the process again, experiencing the same file generation.
So I am going to say it's still an issue with the new client. However, it's still unfinished so maybe it is something they will get fixed.