The first Royal Opera House production to transfer to the West End stage, and Tony Robinson’s first theatre role in 16 years, is a dance-drama version of a children’s book about animals and features a man in a car costume being chased by comedy coppers during the interval. Dumbing down, do I hear you cry? Not a bit of it.

It has been said that Mozart, so prodigiously talented so young, seemed to be merely a vessel through which God, or the music of the spheres, or whichever higher being one chooses, channelled the sounds of heaven. So, too, sometimes, does Balanchine appear to be a vessel through which music is channelled, to take solid form in front of our eyes. And never more so when the music in question is Tchaikovsky.

In 1995 a new avian species with unfamiliar markings, the Bourne swan, drew unexpectedly large crowds to a run-down old Islington theatre. I remember it well: seats in the gods were being worn so tight then that feet attached to long legs couldn't be placed on the ground and, negotiating a tolerable view downstairs at the box office, I missed 10 minutes of the display. Since then the very masculine Cygnus bourniensis has been sighted in unlikely places all over the worldand has now returned to overwinter in a more spacious and comfortable Sadler’s Wells.

This production of Nutcracker, the 10th in English National Ballet's 60-year history, has come in for some stick in the three years since its première. Wayne Eagling, the company’s then director, produced the choreography in rather too much of a hurry, as anyone will remember who watched the third episode of Agony and Ecstasy, the BBC’s 2011 documentary about the company, in which the birth of Nutcracker was definitely filed under agony.

When dealing with the big beasts of the classical repertoire, the Royal Ballet has a history of both playing it straight and playing it very, very well. Peter Wright’s venerable production of The Nutcracker is a case in point: although sticking close to the original scenario and choreography, Wright (along with designer Julia Trevelyan Oman) created in 1986 a show that feels ever-fresh in 2013.

“Comedy in ballet can be notoriously difficult to get right.” So warns the programme note for The Taming of the Shrew, choreographer John Cranko’s 1969 adaptation of Shakespeare, with which Stuttgart Ballet chose to end their run at Sadler’s Wells this week. The note of caution is well sounded in this context; while it is possible for the ballet to be both funny and affecting, the balance is extremely hard to strike, and yesterday's performance at Sadler's Wells was teetering dangerously on the edge of farce.

Stuttgart Ballet, one of Europe's most highly respected companies, is clearly determined to show London its best sides – all of them. Thirteen pieces in one performance is less a mixed bill than a tasting menu, and one that aims to impress: this smorgasbord of pieces were all choreographed for the company, and more than half have not been performed in the UK before.

This triple bill is of works commissioned for the Royal Ballet: Kenneth MacMillan’s The Rite of Spring was first performed in 1962, Wayne McGregor’s Chroma had its debut in 2006 while this is the world premiere of David Dawson’s first ballet for Covent Garden, The Human Seasons.

Can tango ever really be interesting as a pure dance stage show? After all, like most forms of social dance, its truest incarnation is in the fleeting and contingent encounters of the dance hall, the public ball, the open-to-all-comers late night bar. Making tango slick, polished, professional and repeatable enough to put behind a proscenium has all too often made it clichéd and even boring, predictably marketed through the putative sex appeal of tight dresses, twining ankles, and “Latin passion”.

The first time you see a Shechter piece, you feel it, literally as well as figuratively: percussive is a mild word for his forceful choreography, the stamping, churning, yearning of his sweeping shapes and rhythms. Percussive is the music, too (Shechter played drums in a rock band), which he co-writes, and it is played at volumes that make it vibrate through the theatre.