So NJ has only been mentioned so far for NJ 440 being in two pieces and the high exit number on I-76 leaving PA. Here are some other oddities:
NJ 7 exists in two pieces but is signed as one piece. The western piece ends at the Newark border, while the eastern piece begins about five blocks north and east at the county line on the Passaic River. No one really knows the western piece continues south past the eastern piece - and certainly no one knows why.
US 9 has a permanent closure at Beesley's Point. Let's see how long before it's rerouted.
NJ 20 ends as a one-way pair at the top of Paterson... but there's basically nothing for it to end at. Begin/end signage isn't even certain of where the route is. It just sorta starts as you come out from some buildings.
NJ 29, for a few years in the early 2000s, was legislated on a one-way street before NJ figured out the NB side had to follow NJ 165. Now both sides follow 165 (see below).
NJ 36 is C-shaped. It used to be signed east-west on the top and bottom legs of the C, meaning that over the course of driving the route you would reverse direction. "Take 35 to 36 east" was a headache.
NJ 37 had two pieces built that never became part of the route. One is in the middle of the state on CR 539. The other is on CR 524 at I-195, and was kept in the state Straight Line Diagrams as "NJ 524" for a long time.
NJ 41 was the only modern route to be signed as Temporary, and there's still plenty of signage around although the county-maintained route was made permanent because the bypass will never be finished.
NJ 43, until 1988, was signed where NJ 143 is now. Before 1953, all of US 30 was NJ 43. The little spur to Ancora was built as another piece of 43, meaning 43 would have intersected itself - but by the time it opened, the numbering had just changed to remove state/US multiplexes. So 43 in 1954 was completely different than 43 in 1952, yet completely related.
NJ 59 is now signed for all of a short block under a railroad overpass.
NJ 69 is the only 2-digit NJ state highway renumbered after 1953 (to 31).
I-78, as we all know, has traffic signals in Jersey City.
NJ 94 is the only NJ state highway that doesn't pick up as a numbered highway across the border. (It's a 4-digit road in PA.)
I-95, as we all know, has a discontinuity in NJ.
NJ 139 has a lower and Upper (officially NJ 139U) roadway, each 2-way. You can't get directly from the beginning of NJ 139 to the eastbound Upper.
NJ 152 is the next bridge up from NJ 52, but as far as anyone can tell, the numbering is completely coincidental.
NJ 161 was conceived (and numbered pre-1953) as a spur from NJ 3 (then S-3), but 3 was built on a new alignment (in the late 30s/early 40s) instead of along Allwood Road. Surprisingly, 161 was never connected to the actual 3. (It wasn't the only spur disconnected from its parent - NJ 87 was originally numbered as a spur of then-NJ 4, which followed US 9, but a key bridge was never built to Absecon.)
NJ 165 is (now) entirely duplexed with NJ 29, and it's unsigned. Why is it still around?
NJ 167 exists in two pieces. A mile and a half was decommissioned that is closed to all traffic, and the remaining gap consists of bridges that have long since disappeared.
NJ 182 ends catty-corner at NJ 57. It's where NJ 24 used to end, and any hope of extending 57 eastward has long been abandoned, so 57 should have absorbed 182.
NJ 413 is the only NJ state highway to not be state-maintained for any part of its length.
I-676 ends at the PA state line and is discontiguous from the Vine St. Expressway. Technically, it should be I-176, which may be why the number 176 was skipped in state route assignments. (Everything else from 151 to 185 was used at some point, although 178 was never built - 176 wasn't even reserved in legislation, which is very unusual, as NJ tends to reserve numbers even if it won't ever use them.)