Happy Days: Most of the time, the series was true to its roots and played 1950s music in the background. Enter Suzi Quattro (Leather Tuscaredo), who – when she performed – always performed in her late 1970s style. This included her ballad "Find Strength in Your Friends," which she sang using a very 1978 music bed in the episode "Richie Almost Dies" (under which clips of Richie played), an episode that was set in 1959.
P.D.Q Bach ignores the fact that what we think of today as "classical" music actually happened over several centuries and is divided into distinct stylistic periods. Peter Schickele is quite aware of this, but ignores it in favor of parodying as many different things as possible, and lampshades the eclecticism of PDQ's style many times. Then there are the anachronisms which are more obvious to the layperson, such as "Iphigenia in Brooklyn" or the "Bluegrass Cantata" or "Classical Rap" (though Schickele claimed to have altered the original lyrics of that one).
In Brazil this trope is better know as "Samba do Crioulo Doido", after a song, roughly translated as "The Crazy Nigger's Samba". It is about a Samba composer that had to learn some Brazilian history because law dictated all Carnival music had to be based on it (Truth in Television). When asked to do something about the current politics, he goes insane and writes a Samba whose lyrics mixes several important Brazilian history figures from different centuries in a story where nothing makes sense.
The video for ''Glukoza's Schweine'' is all over the place. The Pig Army (clearly a Nazi parody) is armed with G43's, MP 40's, M G34s, Zeppelins, Triplanes, Sd.kfz 250's, and Renault FT's. Meanwhile the Rebel Army Leaders use a G36, a Kalashnikov, an RPG-7, 2 MPL's, a Vickers MG, giant War Elephants, and Pterodactyls. The Rebel Army itself is comprised mainly of Samurai with some Ninjas using swords and pistols respectively.
The Italian progressive rock group Jacula has one weird example - in the mid 1980's they re-released their debut album In Cauda Semper Stat Venenum, supposedly originally released in 1969. The audio production however is very consistent with that of mid 80's Doom metal, and the album also includes the use of samplers (which did exist in the 60's, but their use certainly was not widespread), most notoriously a loop of flowing water that was also used in former band member Doris Norton's 1984 album "Personal Computer".
Not even Satan is immune to this trope. The Rolling Stones' Sympathy For The Devil includes the boast "I laid traps for troubadoures/Who get killed before they reach Bombay" [presumably in a TARDIS].
The novelty song Grandad (a 1970/1 UK hit for Clive Dunn) has the titular grandad reminiscing about his memories of growing up in the old days. Judging by the mishmash of references, his childhood lasted from about the 1840s to the 1940s.
'Hail Caesar'by AC/DC- The lyrics clearly refer to the assassination of Julius Caesar, but apparently the killing started in the Colosseum despite the fact that the Colosseum wasn't built until more than 100 years later.
The video for "Stand and Deliver" by Adam Ant mostly has a 17th or 18th century look, but with several unexplained modern elements.