Continuity mistake: Cooper drops a coin onto the binary sequence in Murph's room. In the next shot, the coin has moved.
Continuity mistake: When Cooper is about to leave Murph, a book falls down, and Cooper looks at the bookcase. When Cooper is in the tesseract, the same scene happens and is reacted to. You can see the same book fall down when Cooper is slamming the tesseract when he says "NO NO," but the (past) Cooper doesn't look at the bookcase this time.
Continuity mistake: Coop is consoling Murph about his trip. His watch says 9:07. In the next shot, Coop pulls out another watch to give to Murph. But now both watches say 8:21.
Visible crew/equipment: When Cooper steps into his car, just before the flat tyre, the boom of a microphone is visible in the reflection of the rear window. Also, the top of head of the boom operator is seconds later and remains visible for quite some time. (00:04:57)
Continuity mistake: Midway through the movie, Cooper is said to be 124 years old while in the new galaxy, and at that time his daughter was still a young girl. Later, when he is back in our solar system and waiting for time to find an opening back to his daughter, who is now in her midlife years, he is awakened at the colony off Saturn, and he's told to take it easy because he's 124 years old but his daughter is a very elderly dying woman. Estimating her age at 90, Cooper should have aged a bit more.
Answer: I am not exactly sure what kind of propulsion system is used, however; you must consider that although in our galaxy even the closest planets to Earth take years to travel to, in this alternate universe, the planets may be arranged in a closer formation.