"I'm not allowed to promote anything that I'm involved in. So I just want to have the legal disclosure, you've asked me the question, and I am not promoting any product," Mnuchin said. "But you should send all your kids to 'Lego Batman.'"
Simply as a product endorsement, this would arguably not be an issue, since the explicit point of the relevant law is that executive branch employees cannot use their position or authority to endorse the product, or do so while in the completion of their official duties, not that they can't endorse products (which would be an unenforceable mess), and Mnuchin makes clear enough as part of the joke that he is not endorsing it as the Treasury Secretary, even if it weren't obvious enough from the immediate context in the interview. Given that other parts of the interview touch on more official considerations, one could perhaps argue for a problem here, but it would have to be argued. But Mnuchin is one of the producers of the movie (hence his comment about not being allowed to promote anything that he is involved in) and he had signed an ethics agreement in which he was not, while in the process of divesting from the relevant company, to participate substantially in things with a direct effect on the financial interests of the company, and thus the product endorsement raises the question of whether he had violated the agreement by recommending the movie in a public interview. One can certainly argue that recommending a movie is not a substantial participation in a matter with direct, predictable effect on the financial interests in question, but it does raise legitimate questions.
Senator Ron Wyden raised the question, and apparently sent a letter to USOGE asking for an investigation. (I have not been able to find any copy of the letter.) Given that Wyden was rather vehement in his opposition to Mnuchin's nomination, it is difficult to avoid the conclusion that this was mostly politically motivated -- Senators usually do not spend their time raking over the precise contents of interviews by Cabinet secretaries -- but that does not mean that there is no legitimate question here. And it should perhaps be noted that if, as the news reports give the impression, he only addressed the letter to USOGE and not also to White House Counsel, this was a very limited request -- as I have noted before, the U.S. Office of Government Ethics, despite the name, is not a general ethics watchdog, but an advisory and training office whose most serious possible action is usually to recommend to other agencies that disciplinary proceedings be started (although it can initiate proceedings itself for ongoing violations). In any case, OGE seems to have begun its inquiry, because Secretary Mnuchin wrote a letter to OGE saying that he should not have added the last sentence, that he would be meeting with the Designated Agency Ethics Official, and that he takes seriously the relevant ethical norms.
And Director Schaub seems to have written Wyden that the OGE "intends to give Secretary Mnuchin the opportunity to make good on the pledge." (Again, I cannot find any copy of this letter, either. Given how poor government ethics reporting generally is, this means everything has to be qualified more than it should have to be.) If that's what Schaub said, he is giving a perhaps misleading impression of OGE's actual role in something like this; it's not as if OGE can ethically refuse a plan for future ethical compliance, it's a one-shot rather than ongoing violation so OGE can't initiate any disciplinary proceedings itself, and to recommend that the President formally discipline Mnuchin over it when there is already an offer of compliance on the table would be extraordinarily incompetent -- compliance, not disciplinary action, is the whole point of government ethics law, and disciplining people who are cooperating conveys the message that there's no good reason to cooperate.
Assuming there are no weird twists anywhere, it's pretty much a textbook example of how this is supposed to work.