@SarahSon: I believe the judge in a civil lawsuit would be more likely to dismiss the case with or without prejudice rather than declare a mistrial as we know it. Sometimes a civil case has not "ripened" enough to justify a hearing, so the judge may dismiss the case without ruling on any of its merits. This way, the plaintiff can wait for more evidence of wrongdoing to emerge before filing a new claim.
The judge can also decide that the plaintiff doesn't have a provable case at all, or else he or she is suing the wrong defendant and should file a new claim later against the right one.
Unlike criminal trials where there are dozens of legal procedures both sides must follow, civil case are mostly determined by the preponderance of evidence. The plaintiff doesn't have to be a great lawyer, just bring enough proof to tip the scale in his or her favor. Mistrials are generally reserved for serious misconduct by attorneys or a jury's inability to reach a verdict.