There was a patent case over the DOS port by Unlimited Software, the porting division of Distinctive Software. Accolade, for whom Distinctive had written The Duel: Test Drive II sought a preliminary injunction against Distinctive Software. It did not deal with the general look of the game, but rather the underlying source code.
Distinctive used some of the underlying "computer code" from The Duel for the OutRun DOS port, which Accolade challenged as an infringement of their copyright. Distinctive argued that these were standard libraries and routines, re-used in different games only for the sake of not having to reprogram them. Also, they claimed Accolade never contemplated the transfer of copyright in the library codes and, even if it did, the codes were not subject to copyright protection in the first place.
Ultimately, Accolade lost the case because the licensing agreement only referred to the concept and design of the game, but not the underlying codes.
The full case can be read through a link in the related links section.
The classic red racer you use in the game is quite obviously a convertible Ferrari Testarossa (right down to the "Cavallino Rampante" logo featured in the back of the car), however SEGA had not licensed the likeness of Ferrari products and got into a series of legal issues with Ferrari. The eventually settled but it wouldn't be until OutRun 2 that the car would become an "official" Ferrari.
A special edition of "Outrun" on cassette for Commodore 64 was bundled with a cassette containing the music from the original arcade game. The intention being to be listened to while playing the game!
Second game Sega made in the 80's that used "Super Scaler" technology.
The PC version has undocumented support for the Tandy TL/RL/SL series; there are a few digitized sound samples that can be heard if the joystick is not chosen to play the game (since the TL/RL/SL couldn't play digitized sound and access the joystick at the same time, due to a rediculous design flaw).