Make note of the real ser# on the receipt,,the date & times you contacted the FFL in an attempt to clear up the log problem and initial & date it.
Keep receipt in a safe place.
Like BaldEagle1313 says,,a bit of CYA goes a long way.
Unless there's some State law regarding registration by ser# which I doubt, then your only concern may be the one in a gazillion chance the gun is already listed as stolen in NCIC by the real ser#.
If that, and for any reason it's (real)# is run by LE in the future,,you'll be relieved of possession the gun of course. But you'll have a reason for why it's in your possession in the first place and not be a suspect.
You're 'ammended receipt' is going to help to explain to LE that you really really did buy it from a LGS,,they just didn't put the right ser# down. Could be years from now.
The LGS records are forever going to list it by the assembly # and no one will ever find it in their records by the real ser#. They will by assembly #.
It's a real long shot at happening, probably a totally mute point,,but only takes a minute to note,,then don't worry about it. You did what you could.
The FFL should know better and be open to correcting clerical mistakes in paperwork.
That's where most violations come from in ATF compliance checks.