One of the biggest negatives is not specific to working for a dragon, but will almost certainly come up more in that circumstance, and that is "the other team". Being paid big money for an easy job is usually foreshadowing of this.
It may not be obvious at first, the other team swoops in after the runners make their getaway, with other objectives. This usually comes to light when the news starts reporting things the runners didn't do, as part of their runs. Or maybe the target squashes the publicity, but gets a mad on for the unknown runners who did the extra job, and someone gets paid to hunt them down... and finds the PCs first.
Eventually, the other team may have cross purposes. The runners pull a hostile extraction, and are instructed to secure the "package" at a safehouse, signal completion, and then get out. Then the other team goes in and does a messy-as-possible hit on the target/package. And the WTF-bomb goes off.
Eventually, the other team is going to get tasked with cleaning up the runners themselves, and/or vice versa. Don't be surprised if there's a third party there to make sure there are no winners, which may be an entirely new (and rather green) crew, whose own clock is now ticking.