In all the problems I’ve mentioned, there are ways to get to the bottom of and mitigate the likely consequences. In the case of a client trashing a previous designer, I’d suggest asking the client to explain why the previous designer was incompetent.
If the problem turns out that, for example, the designer sent a 200-page catalog off to the printer with no bleeds and with all the photos saved as .PNGs, yeah, that’s a legitimate complaint.
On the other hand, if the client is vague about why the previous designer was bad or mentions nonsensical problems or says he or she has a history of hiring designers who turn out to be worthless, that points to a problem with the client.
Even when the client can list specific problems with a genuinely incompetent designer, this still points to an issue with the client that needs to be considered when working with that client. That problem being that the client was naive enough to hire the bad designer in the first place. So in that case, maybe the client really did think he could get his promotional brochures done for $25 on Fiverr. Maybe the client is a real cheap skate and just doesn’t want to pay enough to hire someone who knows what she’s doing.
So in the case of a naive client complaining about a genuinely incompetent designer, it’s still a warning sign in that the whole fiasco indicates that the client is likely naive about working with designers. Walking away from naive clients isn’t warranted, but that naivety is something to consider when determining how best to work with that client.