Factual error: Under US law neither Peter Lowenstein nor Oscar Grace would be allowed any level of participation in the investigation, arrest and prosecution of Ned Racine. Both have a highly visible social relationship with him, which disqualifies them from having anything to do with a criminal case against him. In fact as soon as he became a suspect in Edmund Walker's murder they would both be officially 'warned off' - told not to contact him again for any reason.
Factual error: Regardless of how bad an attorney he is, Ned Racine must surely know that his acquittal for murder is a shoe-in. It's very doubtful that the prosecution would have even held out for remand in his case, and in fact they probably would not have even charged him in the first place. The fact that his fingerprints are on Edmund Walker's glasses is irrelevant. He and Racine were seen in public together, notably in the restaurant, and he freely admits to being in Walker's house. He could have handled Walker's glasses on any one of these occasions. The conversation Racine has with Ted about building the firebomb cannot be used in court, as Ted fires Racine as his lawyer at his second meeting; everything from the first is covered by attorney-client privilege. Maddy obviously isn't around to give evidence, and the yearbook entry Racine finds throws suspicion on her (and away from Racine) immediately. There are no witnesses and no forensic evidence, in fact there is nothing to support the prosecution case except a vague suspicion based upon his having had an affair with the widow-to-be. No court in the US would entertain the case for a minute.
Factual error: When Lowenstein meets Racine on the pier he proceeds to commit a series of appalling breaches of legal regulations, if not the law itself. He tells Racine - a man he acknowledges as a suspect in the murder case he is discussing - about the progress the investigating police are making, the nature and direction of their enquiries, the names of people they are questioning, and the vital importance of a missing piece of evidence. There is nothing in Lowenstein's character that would suggest that he is so unbelievably stupid to do something like this! He would be fired for divulging such sensitive information, and he is handing Racine a Get Out Of Jail Free Card - if the judge didn't dismiss the charges against him, he'd be obliged to declare a mistrial.
Answer: I noticed the problem of the introduction, also. It seemed like a major plot hole to me. There wasn't any material in the movie to support blackmail, etc by the real Matty. I hadn't thought of her possibly being in on the scam. If not, why wouldn't the real Matty have immediately blanched when hearing herself be introduced with the wrong name? So far, I agree with the OP's suggestion.
The real Maddy was at the house when Ned arrived. Presumably, she had already discovered what "Fake Maddy" was up to. It looked like Fake Maddy (Turner) gave the real Maddy a check, presumably a payoff to keep quiet. The real Maddy may or may not have known exactly what Fake Maddy was planning, but went along with being introduced as "Mary Ann." Also, the movie deliberately leaves details vague because it is a big plot twist at the end when Ned, and the audience, learns that Fake Maddy is really Mary Ann.
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