What does Mrs. Higgins mean when she speaks of the "problem" Eliza presents?

The problem, according to Mrs. Higgins, is that the men's project with Eliza, while clever, cannot work because no skill in pronunciation or fancy dresses can change the subject matter of what Eliza talks about. The content will trump the style; she will always give herself away. Like Mrs. Pearce, she also disapproves of the fact that Eliza lives in the house with the two men. Moreover, she complains that Pickering and Higgins are treating her like a "live doll."

Act III also brings a sobering touch of realism back to the play. Standing alone, the bet between Pickering and Higgins seems amusing, worthwhile on humanitarian grounds, and intellectually and practically challenging. Taken in the context of society more generally, a stance which Mrs. Higgins emphasizes, the process is potentially dangerous. The primary function of genteel ladies at this time was to secure a safe and lucrative marriage for themselves, a fact of which we are reminded as Clara eyes Higgins. She views him as marriageable not because she loves him, but because she has calculated thatshe would be a "good catch" monetarily and in terms of his position in society. Eliza has already been made dangerous, however, because she exists outside of this market. Because of her background and lack of pedigree, she is unmarriageable, no matter how charming she may seem. Changing her accent and manner of dress ultimately will cause confusion because it will come out that she is taking part in a slice of society of which she cannot become fully a part-Freddy will only be disappointed. Mrs. Higgins puts it bluntly when she complains that Higgins has given Eliza the "manners and habits which disqualify a fine lady from earning her living without giving her a fine lady's income." The change of setting from the isolated Wimpole Street laboratory into a "society house" makes this shift even starker. Eliza is becoming too good for her old society, and she is not yet good enough for her new society. This gap in the experiment is troublesome, and something must be done about it. It is not clear, however, that the men are fully aware of the problem or that they have a viable solution.

Although Eliza can tell an entertaining story, Mrs. Higgins points out that the girl is far from being ready to be presented in public. She certainly lacks the poise and clothes to present her to high society.