Make sure your downloads app is not disabled or try clearing its cache and data within the app manager in phone settings. Make sure you know where the message/pic is supposed to be saved...might be (if equipped) the SD card is having issues with reading and writing. Perhaps try a full cache wipe (not factory reset) of the phone. Without knowing exactly which Note you have, most Samsung Galaxy phones' cache can be accessed via:
Press Power, Volume Up and Home simultaneously
Wait until the phone vibrates and then release Power and Home
You should now see the recovery screen. Use the volume buttons to move and select Wipe Cache Partition.
Press the Power button to confirm.
Select Reboot System Now and again, hit Power to confirm.
Wait until your Note reboots and hope it’s fixed the problem.