I wrote my master's thesis in history on Frances Cleveland and public perceptions of her role as first lady. One of the chapters focused on the wedding of Grover Cleveland and Frances Folsom, and in researching this portion I read as much newspaper and magazine coverage as I could get access to. This included major papers such as the New York Times, the New York Tribune, the Chicago Daily News, and the Washington D.C. Evening Star. I also examined popular mass-circulation magazines, including Ladies Home Journal, Harpers Bazar, Puck, and Frank Leslie's Illustrated Newspapers.

All of these publications devoted extensive space to the White House wedding, and in none of them did I encounter any hint that there was anything strange about the pairing of Grover Cleveland and Frances Folsom. In fact, the general sentiment was summed up by an article in the New York Tribune (titled "Mr. Cleveland's Devotion to His Ward") that described it as "like a story book or fairy tale." Up until the announcement of the engagement, Cleveland had had a reputation for being rather gruff and unsociable, and people seem to have been genuinely charmed by the revelation of his romantic side. As one writer for the Chicago Daily News observed:

"There is something characteristically American about the merry yet respectful, jesting yet sincere, interest our people take in the nuptials of the president. Every bit of gossip concerning his courtship and the life, appearance, and character of his intended is discussed with as much avidity as if she were to be the bride of some personal friend. The people do not stand afar off and watch the preparations for the marriage as if it were to be a pageant of royalty. They are not restrained by any awe of the president's high office from showing their curiosity about his persona affairs. They feel that he owes his elevation to their suffrage, and they wish him joy and tender him advice with all the freedom of equals."

Of course, this was just what was being said publicly, but I have no reason to think private opinion was drastically different. Frances was an enormously popular figure throughout Cleveland's first term in office, and she was joyfully welcomed back to the White House in 1892. By that time the Clevelands had a daughter, Ruth, and would welcome a second child in 1893, completing the picture of domestic felicity.

Frank (Frances) Folsom's age at her marriage to Grover Cleveland was something noted by the press, absolutely. However, any criticism seems to have been rather mild.

One article, printed in multiple newspapers including (here) the Indianapolis Sentinel, merely said:

She is the daughter of tbe former law partner of Mr. Cleveland, and is spoken of as a lady of great brilliancy, and one who would be an ornament to the White House and to society as well.

She is perhaps a trifle young for an old fellow of forty-eight, for as the President celebrated his birthday on Wednesday, it is hardly worth while to try and conceal his age longer.

Her age, if so delicate a subject may be touched upon, is probably about half that of the President.

She is spoken of as very handsome...

Even when a newspaper column mentions her age, there is nothing said about their earlier relationship. I'm especially a fan of this clip from an Iowa paper I found online, in which the author discusses Frank's childhood handwriting and even her childhood nickname with nothing but approval for the woman...and comments (apocryphal or not) about how her handwriting was setting the trend for local women.

Grover's 1923 biographer, Robert McElroy, repeats an unsourced, possibly apocryphal story about the president's reaction to the rumors circulating in advance about his possible marriage...to Frank's mother:

I don't see why the papers keep marrying me to old ladies all the while--I wonder why they don't say I am engaged to her daughter.

I am not sure I would take this particular story seriously, especially because McElroy doesn't cite it beyond "an old friend and her daughter." On the other hand, I've never seen any disagreement that the press did expect Grover to marry the widow Emma Folsom, not her daughter.

This makes some modern scholars' argument that Grover began a romantic relationship with Frank and (especially) married her as an election/reelection strategy...hm, interesting. On the other hand, that such an argument can be made in the first place likewise points to a general public acceptance.

So you can see the marriage did not quite seem the most natural, but wasn't a widespread problem. The media's utter infatuation with Frank herself might have helped matters, as probably did the fact that Grover had already beaten one sexual scandal (a) by owning up to it, and (b) it still being less bad than the competition's political sins (c) probably because the parts of the sex scandal that reflected truly poorly on him depended on the word of a woman.

And by the time Frank Cleveland was departing the White House along with her husband, "a trifle young" had become a good thing:

A modest, robust, enthusiastic girl she entered the White House. The entire nation was interested in her. It delighted in her youth and beauty.

...It is, however, noteworthy that eleven years later, the Chicago Chronicle was remarking not just on her youth at the time of marriage but remembering that people had talked about it.