Depending on what version it is, Drosselmeyer is usually depicted in one of several ways:
Productions such as the 1983 Pacific Northwest production play him as a reclusive and mysterious, and somewhat creepy, figure who hates to see Clara grow up and longs for the days when he could impress her younger self with his stories and toys. This is shown when Clara finds more interest in the titular nutcracker than in Drosselmeyer’s clockwork palace, making him jealous.
Other productions play the character straight, making him a playful trickster but also a caring and kind Grandfather figure to Clara.
Clara's journey to the kingdom of sweets has been interpreted as a metaphor for sexual discovery.
Or Pas De Deux. It's incredibly romantic, and was written on a dare to write a piece of music that played the scale in order.
Ballet critic Arlene Croce pointed out the particular chords bear more than a passing resemblance to a very common Russian Orthodox funerary piece. The theory goes it was in part a musical tribute to Tchaikovksy's recently deceased sister Aleksandra.
Mother Ginger is very much this. While the other dances in Act 2 are frequently lovely balletic displays, Mother Ginger and her children are played chiefly for laughs. This is likely the reason the Royal Ballet production cuts this number out entirely.
The 1983 Pacific Northwest Ballet version filmed as Nutcracker — The Motion Picture (1986) had set and costume designs by Maurice Sendak and also takes on coming-of-age themes. Clara is played by a young girl in Act One, and Drosselmeyer is, as Roger Ebert and other critics noted, at least a bit of a Dirty Old Man who plunges her into the battle of the Nutcracker and Mouse King. Once the King is killed, the now-human Nutcracker and Clara are played by adults. They travel to a kingdom ruled by a pasha, played by the same actor as Drosselmeyer, who is jealous of their romance and tries to distract her with his dancing subjects (who replace the Land of Sweets characters).
Broken Base: Nutcracker has been around long enough, and has acquired enough different variations, that a number of topics will set off near-instant flame wars among serious ballet nerds:
The theming of the Land of Sweets characters: should they be themed to different sweets and drinks, or just to the countries that match their musical styles? Arabian, or Arabian Coffee? Spanish, or Spanish Hot Chocolate? Russian Cossacks, or Candy Canes? Chinese, or Chinese Tea? Shepherds/Shepherdesses, or Marzipan? Express an opinion, and then duck.
Should the Nutcracker Prince and/or Clara dance with the act II divertissements, or merely watch?
Should there be a romance between the Nutcracker Prince and Clara, or should they just be friends?
Should Clara dance en pointe, or on the flat? Should she be danced by an adult ballerina, by a teenage girl, by a real child, or should she be a child in Act I but then "magically transformed" into an adult ballerina for Act II?
The All Just a Dream ending or the reunited-in-the-real-world ending or the apotheosis ending?
'Clara' or 'Marie' or 'Masha'?
Should the Sugar Plum Fairy dance the grand pas de deux in Act II with her Cavalier, or should Clara/Marie and the Nutcracker Prince do it? This tends to be a hard split between adherents of the Russian version (typified by the Mariinsky and Bolshoi ballets) and adherents of all other versions.
Keep Mother Ginger and her polichinelles, keep the music but change the act, or cut the whole thing?
And on, and on, and on...
Epileptic Trees: That the story is really about female sexual maturity, and the beautiful Land of Sweets is an allegory for eroticism.
Esoteric Happy Ending: Some versions simply end with Clara and The Nutcracker riding off in a magic sleigh pulled by reindeer, with no indication of whether Clara's fantasy was All Just a Dreamor not. This is parodied in the comic strip FoxTrot in an arc where Paige plays Clara in a dream.
Gateway Series: This is many people's first introduction to the ballet as a whole, especially for kids because it's quite family-friendly fare, and for non-theater-goers it's a part of holiday festivities. It's acquired a reputation as "Baby's First Ballet," not entirely unfairly as it's likely to be the first ballet most people see these days.
Germans Love David Hasselhoff: Has become a stalwart in American ballet since the 1940s with performances usually held during the Christmas season.
Some versions, like the Marinsky and American Ballet Theatre versions, apply this to the "Waltz Of The Snowflakes" segment, where the snowflakes take on an almost menacing tone and convey the sense that Clara and the Prince are trapped within a potentially fatal snowstorm. The Marinsky version is literally this—lighting of the scene is very dark, the snowflake dancers are clad in black, and the singing is done by an actual children's choir onstage—the ghosts of children who have frozen to death in these woods in winters past.
The Mouse King can be very scary, especially in productions where he has seven heads.
Older Than They Think: Many believe (for better or worst) that Balanchine came up with the concept of the Trepak divertissement featuring a hoop dance, rather than using the more common Cossack-outfitted dancers. In fact, the hoop dance was actually from the original 1892 version, which Balanchine reconstructed from memory; if anything, the hoop dance is actually more faithful to the original.
"Dance of the Sugar Plum Fairy" is one of the most well known segment(s) of the ballet. If any work uses music from "The Nutcracker", it's often this piece. Sometimes it's parts of "Dance of the Mirlitons".
"Russian Dance" as well - Part of this is due to Fantasia where its movements fit the music like a glove. Another part is the music is very catchy
"Chinese Dance" is also fairly well known as well - despite some Values Dissonance. It also doesn't help that it also plays near the Russian dance.
"Waltz of the Flowers" is also another popular piece of music from this play.
Slow-Paced Beginning: One of the main criticisms of the ballet, both at its release and today, is that it takes a while for there to be any serious ballet, since the first act is largely a house party limited to partner dancing, with the principals not really appearing until the second act.
Sweetness Aversion: A common criticism from serious ballet fans, especially ones who are tired of seeing companies re-stage The Nutcracker every year rather than embracing edgier (though less commercial) fare. Give them their due; the entire second half of the ballet does take place in the "Land of Sweets." Thanks to the number of dancers now using social media, it's hard to avoid noticing that some of them are often not so fond of the ballet, either, especially in companies where they may do nothing else for two months straight. Even Tchaikovsky called it "fluff".
In the 1993 film version, the mice are clearly saddened by the death of their king, and carry away his body and sword. Despite being the bad guys, it's not hard to feel a little bit of pity for them.
Any version (e.g. Baryshnikov's, or the Royal Ballet's) where the Nutcracker has a Disney Death at the hands of the Mouse King and Clara cries over him just before he transforms into the Prince.
Values Dissonance: Depending on how much the national divertissements in the Land of Sweets play on stereotypes.
The Moor in the Baryshnikov version was done in Blackface.
Vindicated by History: Although the music was well-liked, the ballet itself was never very popular until the mid-20th century, when it practically became a Christmas tradition.
, Dance of the Sugar Plum Fairy