What would be the typical "gotchas" involved with scripting all the data to migrate a 2014 SQL server database to 2012?
A counter question would be why are you downgrading from 2014 to 2012 ?
Now lets address your question, if you are just downgrading from 2014 to 2012 with same version (standard --> standard) then there should not be any problem unless you are using something that is new in 2014 and is not present in 2012.
Downgrading an Enterprise edition to standard edition, you have to remove / disable all the enterprise features and then downgrade.
Downgrading is always a pain.. You have to script out the skeleton (schema, objects, etc) and then recreate it on 2012 and then use
BCP OUT / BULK INSERT IN to get the data into sql server 2012. I have used the script that I wrote for a similar task.
Have there been times of "Oh man, didn't see that coming" some time later when you run into some type of conflict because of the migration that wasn't caught previously?
You have to thoroughly test out the entire process before you attempt to run it in PROD. The script that I have mentioned will assist you.
With business critical data, is this unwise to do? It's a cost/benefit situation of upgrading and licensing for a newer SQL.
I don't see a reason for downgrade. I would suggest you to be on the latest version of SQL Server. Its worth the investment. Since your data is "Business Critical", I would suggest to go with SQL Server 2014.
Also, what you can do is you can set up replication from sql server 2014 to sql server 2012 or just install another instance of sql server 2012 on the same machine (if you have enough capacity and resources).
Note: "migration" is misleading.. it should be downgrade. I use migration when moving from a lower version of sql server to higher version of sql server.