I recently noticed that opendkim on my mail server is objecting to DKIM signatures from a client, saying their key is insecure. It may be that that's due to lack of secure DNS (confirmation?) but I also noticed that the signing algorithm is shown as a=rsa-sha1, and with the move to Deprecate SHA-1 in other contexts, I'm wondering how urgent this is for DKIM?
It is now feasible to brute-force SHA-1 hashes. Am I correct in thinking that this would need to be done for each message an attacker wished to forge the signature for, without being able to re-use that work for the next message?
Yes, as of January 2018, SHA-1 is deprecated as per RFC 8301. From the perspective of server administration of DKIM signing keys, the RFC will take precedence because the receiving server will fail the authentication test when signed with SHA-1, and is expected do so regardless of actual computational threat level.