Is it possible to flag a delinquent account?

In the Family record, on the Summary tab, you can designate a family as a "Problem Account" and specify the reason in the Notes field on the Misc. tab. 

When set to yes, the Problem Account label turns red, and within Global Search, this account row is colored red. This can be used to help your staff be aware of a problem and where to read more about the issue (Family record > Misc. tab > Notes field).

Block Registration for Problem Accounts in Parent Portal

You can block families from registering for additional classes in the Parent Portal (under the Gear icon > Settings > Parent Portal > Settings tab > Class Enrollment Settings > Prevent Problem Families from enrolling) check the check box and Save Changes.