It's only to be expected that religions that evolved thousands of years ago would include reams of superstitious nonsense along with any positive ethical and community values. To a large extent most forms of Christianity have removed the most egregious relics of those days, a process begun in the Reformation and continued in our secular society. Though Islam is only 1200 years old it contains reams of superstitious nonsense.
Islam also has an ongoing Reformation. The Wahhabist/Salafist movements are conducting a violent, puritanical crusade against "accretions" to Islam. However Islam is full of bog standard superstitious nonsense deeply embedded from it's first days.
The Black Stone(s), the holiest rocks in the world. If at all possible Muslims need to travel to Mecca for the Hajj and circle a cubic building (the Kaaba) holding a cemented-together smashed stone seven times and if possible kiss the stone with each counterclockwise circumambulation. Muslims believe the Kaaba was first built by Adam, who placed the Black Stone in it. When Abraham and Ishmael later rebuilt the Kaaba, the Angel Jizreel (Gabriel) returned the stone to them. The Black Stone was the only idol allowed to remain in Mecca after Muhammad's conquest. In 930, the Qarmaṭians sacked Mecca and Medina in 930. They filled the Zamzam Well with corpses of Hajj pilgrims and stole the Black Stone, using it as a urinal. They held the Stone to ransom but in 952 returned it when the Abbasids paid up.
The Stoning of the Devil is one of the most important rituals of the Hajj. Pilgrims spend days pelting devilish stone pillars with stones and finish with a final circumambulation of the Kaabah. Muhammad got some Biblical details confused, God told Abraham in a dream to slaughter Ishmael as a sacrifice to God. Ishmael being a good Muslim told his father to do the dirty deed. The Devil appeared three times to Abraham to tell him not to kill the boy but Abraham stoned the Devil with seven stones each time. This is not the story as originally written in the Torah or Old Testament.
The Ride To Heaven: One night Muhammad was cut open and his heart removed and washed out with Zam-zam water in a golden tray. He then rode on his magic horsey al-Buraq and shortly landed in Jerusalem and led prayers with a posse of dead prophets. Al-Buraq then leapt up and took Muhammad to the 7 heavens where he chatted with John the Baptist and Jesus and went on to a Holy Tree …
Muhammad believed most of the generally held superstitions: the "evil eye," evil spells, black magic, djinns, demons, etc. These days belief in possession by jinn, witchcraft, and the effects of the "evil eye" are still mainstream Islam and are believed to cause many deaths. Muhammad believed he'd been affected by the evil eye and the witchcraft of … you guessed it … a Jew. He thought he'd been fucking his wives but it turns out he was just a deluded old man. - Bukhari 71:660
Muhammad certainly came up with some weird superstitions that are all his own: Satan causes yawning (Bukhari 73:245), Oversleeping is caused by Satan pissing in your ear (Bukhari 54:492), Keeping a dog as a pet will cost you 2 celestial rewards taken off your good deeds (Bukhari 67:389), You should only hold your penis with your left hand when doing anything therewith in the toilet (Muslim 512), You should only wipe your arse with an odd number of stones after shitting (Bukhari 4:163), Satan sleeps in your nose, so water should be snorted each morning - pretty impressive, that's a lot of noses at once (Bukhari 54:516), Spitting over the left side of the bed prevents nightmares (Bukhari 87:115).