How to check the number of files in a folder without counting them

Short of getting a different mail client on your iPad I can get you more than half of the way there.

Set up gmail as Microsoft Exchange server (leave the domain blank, add user and password and let it try to connect. When it fails, use m.google.com for the server and you can choose mail, calendar, address data to use ActiveSync)

Once the first mail sync starts, you can then choose days to sync and which subfolders will have push enabled. The mail badge count still only reflects unread messages in the Inbox, but you will get the mail notification sound/vibration for any new push message arriving in your selected subfolders. Your iOS device will be ready to go when you tap into the folders that have new push messages.

Unfortunately, I don't think that's possible, since badges are rendered using code that needs to be included in the app: Finder would need to integrate the code to tell its badge to change.

Consequently, third party apps, in theory, could get the file count of your Downloads folder, and they could code a badge to display it, but they wouldn't be able to access the Finder's dock tile objects: each app can only access their own, and app icons can't only be placed on the area of the dock reserved to folders and document aliases.

I couldn't find any utility that could solve this issue. I'm sorry. It's a great idea though, and I would totally love it if someone proved me wrong and posted an app capable of doing this, for I too have a pretty messy downloads folder.

The only way I found to get easily the item count is the status bar. Perhaps though, you could do a workflow in Automator or Apple Script Editor. I know Automator can make folder actions, which are run every time a file is added to a folder. It would just be a matter of keeping a count, I guess.

Sources: A bit of research on desktop badges in Apple's developer documentation. The examples there all show the desktop tile object needs to be accessed directly within code.

Hope it helps! And good luck.