This is not possible to capture the failed syncs, excepted if the failure comes for the sync filter (see "Sync with Marketo" mysteries part 3-How to know a record has stopped sync'ing )
For the rest, I have quite covered here: Marketo / salesforce integration needs a serious overhaul, don't you "sync"? so, just vote for the missing features
The last possibility would be to use the API to extract the logs, analyze them and update back the leads to trigger what you want.
But you probably can capture invalid emails directly in Marketo with a smart list, can't you? then you would use this smart list to avoid syncing them with a choice in you lead management campaign flow step.
We run a campaign and smart list to check such leads and then fix the issues.
I occasionally see sync failures that result in sales not receiving a new lead because owner isn't assigned. I'd like to get the owner assigned and into the hands of sales ASAP rather than wait for a cleanup operation that only happens once a day.
What's the recommended approach for handling these cases so the sync can happen as soon as the root cause is addressed (usually some glitch on the Salesforce side that need time to resolve)?