Technology Marches On: When he's back in the 1920s, Max's ex-partner — who comes from the early years of the twenty-first century — listens to a portable music player. However, since the movie was made in 1994, it's a CD Walkman. Apparently, he never got around to updating to an iPod.
It should be pointed out that the device in question was a Sony MiniDisc player, which in '94 was being touted as the "wave of the future" in personal listening devices. Unfortunately for the filmmakers, this turned out to be a major Failed Future Forecast as well as a case of Zeerust; in 2004, you'd be hard-pressed to find anyone who'd even heard of the MiniDisc audio format—it was as dead as the Beta VCR, and Sony abandoned the format entirely in 2013.