This is the biggest myth of younger physicians and those in residency. I have been on hiring committees and have been making hiring decisions for close to 20 years. (And years before that working with the JAG and DoJ as liaison for military malpractice cases.) Let me tell you, NO ONE cares about your malpractice record. Unless you are losing 20 cases a year, I and those who I have worked with over this time frame have paid no attention to how many malpractice cases you have, or if you won or lost them.
Now some people are concerned about losing a case for above their malpractice limits. This might have happened once or twice in the US this century, but it is incredibly rare. Your malpractice carrier has a duty to make a settlement offer within policy limits. Now, you may have also heard that in the "American system" each side is responsible for their own attorney fees. There are a couple of exceptions to this, and one has to deal with "offers of settlement." Lets say that your insurance carrier makes an offer to settle for $250K, and the plaintiff rejects it. Then the jury comes back with a judgement for the plaintiff in the amount of $200K. On the surface, it looks like the plaintiff won this case. However, in this scenario, the PLAINTIFF will be required to pay the defendant's attorney fees since they rejected a settlement offer and then received a less favorable judgement. Since the malpractice insurance companies attorney's fees are probably more than the amount awarded by the jury, the plaintiff's lawyer (if they are on a contingency basis) could end up not only being out their costs, but also stuck with a six-figure judgement against them. The bottom line is that a settlement offer is almost always accepted by the plaintiff. Especially since there is little money in them trying to recover anything past settlement limits anyways.
I have a general principle that I have lived by: I don't care what people who I don't respect say about me. I don't care that some attorney who knows nothing about medicine thinks that my care was negligent. I also don't care what a jury of "12 people so dumb they couldn't get out of jury duty" think about the care I delivered. Finally, I don't care what anonymous "reviewers" on the internet think about me. I do know physicians who get all tied up in knots about this kind of stuff. I think they are idiots and have told them that to their faces.
So to summarize: Unless you are getting 20 suits a year, or the suits are linked with another problem (you faked your residency graduation, or you have a substance abuse problem) no one cares about them when it comes to hiring.* It is also incredibly rare for a judgement to come back above policy limits. (If it does, you will have a good case against your malpractice insurance carrier.) Yes, you can point to a case or two where it happened, but there are also cases of someone getting $1M because the sun flashed off your watch-face and caused them to run into a pre-school. Finally, don't worry about what idiots say about you. You will be much happier.
*OK, like the above judgement jury verdicts, there are probably a hospital or two out there with a low-level employee who might screen these out, but it is rare, and when they are found out, they are usually fired. But the general principle still holds, it is incredibly rare, and you probably wouldn't want to work there anyway.