Whose lawyer, and what was the blunder?
The Schindlers' lawyer. Instead of filing the opening plea of a de novo trial, he filed what was essentially an appeal of the state court ruling. His arguments all hang on alleged procedural errors by Greer.
The whole point of having a de novo trial was to get the facts re-heard, with the goal of having a different judge reach a different conclusion regarding the "fact" that Terri Schiavo's preference is to die in this circumstance, and the "fact" that Terri Schiavo is in a persistent vegetative state from which she will never recover.
CNN wrote about the trial procedings, (I don't have that link & I'm not going to dig thru a week's worth of coverage to find it now) and reported that the judge asked the Schindler's lawyer for case law to back his assertions and he said he couldn't think of any. To make a case, you've got to have references, either to the Constitution, to legislative law, or to previous cases. If their lawyer had nothing to back him up but his opinion, where did he expect the case to go?