Word or phrase indicating incompetence or unsuitability?

Solution 1:

The word you may be looking for is stigma:

stigma, noun

: An association of disgrace or public disapproval with something, such as an action or condition [AHED]

: a mark of shame or discredit [MW]

Solution 2:

I would go with discredited as an adjective, discredit as verb or noun. From TheFreeDictionaryOneline:

dis·cred·it
tr.v. dis·cred·it·ed, dis·cred·it·ing, dis·cred·its
1. To damage in reputation; disgrace.
2. To cause to be doubted or distrusted.
3. To refuse to believe.
n.
1. Loss of or damage to one's reputation.
2. Lack or loss of trust or belief; doubt.
3. Something damaging to one's reputation or stature.

Solution 3:

Perhaps "fatal flaw?". Indead, you can put "fatal" before many constructions in order to turn them into deal breakers. So "fatal black mark" works, and as a bonus, it reminds people of Treasure Island.

Solution 4:

You can use the words "inadequate" , "inefficient" or the phrase "lions led by donkeys" meaning leading to loss because of incompetent and indifferent leaders.