The basic equipment details were probably the same as on 1980/1981, with the obvious additions and slight variations. For this tour, there was a supporting keyboard player (Morgan Fisher in Europe and Fred Mandel elsewhere), which together with the new songs added resulted on three different people playing guitar on each concert (Brian, John and Freddie) as well as three different people playing piano (Freddie, Brian and either Morgan or Fred), a unique occurrence in Queen history. Roger also got a new kit - in chrome finish.
For the North American leg, a Gibson Flying V was added as second spare guitar, which was a wise choice as on 9th August 1982 Brian had a rough night and was uncharacteristically upset and aggressive: after breaking a string on the Red Special, he started playing the Brighton Rock solo with the Birch replica, but got so frustrated with it that he threw it away, and it was smashed in two pieces; from then on, the Flying V would be his spare until the end of the tour.
Two Hot Space songs, Staying Power and Body Language, had the bass line played by Morgan or Fred (Mandel) on synthesiser. For the latter, John joined on second bass doing some reinforcement, and for the former, he played guitar alongside Brian. Brian played piano on Save Me and (Japan only) Teo Torriatte, but after this tour he'd never play acoustic piano on stage again (as of 2012, that is).
Drum kit [sans snare and cymbals]
Snare drums [used alternatively]
Timpani [Roger's Solo]
Gong [hit once at the end of Bohemian Rhapsody]
Electric bass guitars
Main electric six-string guitars
Spare electric guitars
Acoustic guitars [Love of My Life, Crazy Little Thing, Life Is Real]
Acoustic guitar rig
Piano and synthesizers
Electric grand piano
What about the recording sessions?
Hot Space was an unusual album for the band as a lot of the rhythm section in the first side was created by machines (which explains why the live versions sound so much better - they've got real drums!). Equipment used included Linn LM-1 computers for the drums (programmed by the author of the song) and Roland Jupiter 8 for the bass. A lot of people blame John Deacon for Hot Space even though he was the least involved band member on it: on Dancer, Staying Power and the lead single Body Language his bass is replaced by the creator of the song on synth. John publicly expressed his disdain for the album, even calling it the worst moment of the band's career (Popcorn magazine, 1986) - the fact he liked R&B and soul doesn't mean he'd like anything in that genre; if anything, his expertise on the area may have made him harder to please if he felt the result wasn't up to standard.
Other equipment used exclusively on the record included a Hohner clavinet for Cool Cat (where John most likely played the Music Man bass), a Baldwin Double-Six guitar on Under Pressure and a Schecter guitar on Calling All Girls (played by Roger instead of Brian). The sax solo on Action This Day was played by Italian session musician Dino Solera, who was based in Munich and had participated in many recordings at Musicland Studios, sometimes uncredited (as it happened here).