Best way to allow any user to suggest a record for delete?

You can use email field. You can configure it that all emails are sent to you. Also you can set predifined subjests so user have options like

• This business no longer exists
• Information provided is not correct
• This is my business

And hide body and all other field.

Actualy this case is one of those that the email field was created for.

techutopia I would then like to have a list that I can look at and then delete records as appropriate.

This would require to "flag/mark" the record in question. Just some quick thoughts:

A.) Status field is nice, but doesn't help here out-of-the-box, since it could be changed by many users. Not once. Maybe a special Rating-template? Problem: How to generate a proper list...

B.) Re-post feature. User's repost the record admin's homepage only. Drawback: There is no subject/message to differentiate. Not sure how to restrict posts to admin's page.

C.) Comments: Do you already use comments with your records? Core or Type-as-Comments may replace an email. You would have a connection to the record and even a notification. This data could be used to create a kind of "list". Cobalt-Type-as-Comments can be stored in their own section/category, which gives a separate list.
Actually, this is even comparable to this Cobalt forum. The only difference: Answers/posts are visible to admins only.

D.) Relation fields: Add new child as a "flag". Maybe a good alternative, if you already have comments feature in use.

Sergey Actualy this case is one of those that the email field was created for.

@Sergey
Related question: Is there any connection between the email and the record? I mean, apart from the email... can I get the information where it was sent from? Maybe recordID# and/or record URL.

There is record ID and URL in email.