Awesome Note are not available if your iPod software is not 3.0 or later, you can't download to your iPhone/iPod Touch.
You missed Requirements of Application Description on the App Store.
>> Requires iPhone OS 3.0 or later.

To find out which software version is on your iPhone/iPod touch, follow these simple steps.
Tap the Settings icon > Tap General > Tap About to see the version number.

The software version number appears next to version.
Install the iPhone 3.1 Software Update for iPhone/iPod touch.

For more information about OS, visit at iPhone Update or iPod Touch Update

If something isn't working right, try below steps.

Step 1) Restart or Reset iPhone/iPod touch
Turn iPhone/iPod touch completely off and back on.
No data will be deleted. if this solved your issue, you're done.
See Turning on/off and resetting >http://support.apple.com/kb/HT1430

Step 2) Reinstall an app
If an app is not working as expected, you may need to reinstall Awesome Note.
Data will be deleted. Be sure to backup your data by syncing to Google Docs if possible.
Remove this app from your iPhone/iPod touch and download it again.
Once you purchase an application, you can download it without charge.
See Reinstall the application >http://support.apple.com/kb/TS1702  
See Syncing applications from the App Store >http://support.apple.com/kb/HT1977

Step 3) Restore
If for some reason it doesn't solve the problem, you can try restoring your iPhone/iPod touch using the latest version of iTunes.
iTunes creates a backup of your iPhone/iPod touch when you sync, which you can the use to restore from if you need to return to a previously backed up state or if you delete applications.
This backup may fix an error on your iPhone/iPod touch.
See About backups>http://support.apple.com/kb/HT1766

If you failed to upload to Google with error message below
"An error occurred while exporting notes"
"Transferring backup data..." then " Fail to upload backup data."
It was more likely to be issues regarding to Google.

An unexpected error or timeout might be caused by below

1. Google's own problem ( Google has been unstable lately)
    This usually happens when the Google Docs service is down.

2. Unstable net connection
    Make sure your iPhone/iPod Touch is connected to Wi-Fi, and retry.

3. Uploading large data
    Google Docs has a size limit of 500K for notes uploaded to the service.

If you got a message 'Sorry, that file is corrupt, or an unknown file format' in a note,
when you open a note that has been imported successfully,
This error message will occur if Google has some problem.
Please retry.

Password protected notes may be able to be uploaded to another user's Google account.
This will be improved in the next update.
Global password and Full sync will be added.

If invalid ID or password error occur despite you are sure that your gmail account are corrected,
It happens when your iPhone is not connected with internet.
Make sure your iPhone/iPod Touch is connected to Wi-Fi, and retry.

Backup file stores all information about notes, folders and themes.
This is an unreadable text when you open in Google Docs.
When you download this backup to Awesome Note, all is restored properly.
Use Import/Export feature if you want to see the readable text.

If you got error messages below and failed to download, it was more likely to be issues relating to Google.
"An error occurred while importing notes"
"Restorring backup data..." then " Fail to download backup data."

An unexpected error or timeout might be caused by below

1. Google's own problem ( Google has been unstable lately)
    This usually happens when the Google Docs service is down.

2. Unstable net connection
    Make sure your iPhone/iPod Touch is connected to Wi-Fi, and retry.

3. Downloading large data
    Google Docs has a size limit of 500K for notes uploaded to the service.

You can import or export only documents (TXT, DOC, RTF formats) from Google Docs.
These files (PDF, XLS, CSV, ODT, HTML formats) are not available.

The notes imported from Google have been put in All Notes.