Nine clues are not like the others. Solvers must identify the unusual clues and highlight the corresponding answers in the grid. To help with this task, the grid has two unclued entries which hint at what these clues have in common. To make things a bit more difficult, I have added other commonalities, which are not related to the actual answer, to some of the clues. Sorry about that!1 Have fun.
Across
2. (unclued)
9. Expert's muscle slightly inflates in front of street boxing champion (10)
16. Once part of West Asia's cuisine: appetizers, starters, followed by Indian bread (6)
17. Rotation of cakes at the back covered with frosting, mostly (7)
19. Green sign of life (5)
21. Artisan crafted for ruler of Imperial Russia (7)
22. Baths of hot water? Mother can be seen in that place (7)
23. Feeling of apathy let sinner 40 down hearts (5)
27. Cold drink without a drop of Hungarian wine (4)
29. East of Massachusetts, east of Rhode Island (6)
30/32. For one, Manchukuo pioneer's beginning to promote favourite small museum (6,5)
34. Wasted, running about at first, Rachel's – in King's absence – a ruler (7)
36. Prominent Turk unexpectedly groaned (7)
40. Rhode Island preacher briefly backing up Orinoco, perhaps (5)
43. Dad's attempt to make baklava, as an example (6)
44. Suspended half a dozen in ancient Rome, a kingdom of old (6)
46. Temperature dropped in French-speaking city belonging to US (4)
52. Entertain king I have sheltered, essentially (5)
53. Part of shop I ran half-heartedly for one living in the Orinoco? (7)
54. Trade some unusual energies leaving Imperial Russia, for example (7)
57. Musical duo of comediennes appearing in satires regularly (5)
58. Guy with a shirt is a lethargic swimmer (7)
59. Bottom-feeders rip off private eye (6)
60. Slithering biter and horrible king's eater (5,5)
61. Properties from eastern Connecticut and Rhode Island? (7)
Down
1. Drug company to write describing geographic variety of species (7)
2. Enthusiastic follower of a nationalist subsection (3)
3. Scratching head – jinxed, bad sign (5)
4. Island retreat: 26 down undressed by topless man (5)
5. I complain about woman (5)
6. Foul up a print somewhat (2,4)
7. It can be post-traumatic forgetting note from paramour (6)
8. True, the son is in poor condition (6)
10. Character in ancient Greek play supported Ionian leaders (3)
11. (unclued)
12. Spade cutting inanimate stick (6)
13. A Native American's (a Pawnee's) head hurts almost entirely (6)
14. Jafe laid out work of ancient Greece (5)
15. Drop auditor's rank (4)
18. God of ancient Greece is showing cooking equipment (4)
20. Centrally produced cookies? New York has one (4)
24. Noisy arguments stir up for the dictator (4)
25. Joyful member in an adventuring group of nine (5)
26. Revolutionary extremists in uprising with half of Russia's experts (5)
28. One media device for vehicle suited for off-road use (3, abbr.)
31. US writer takes slightly surprising stand (4)
33. Discovering milk products producing gas (3)
35. Energetic private eye almost catches many running in the opposite direction (7)
37. Male perhaps is Greek starter and finisher (6)
38. Eleven norms regularly included amongst Ampère's laws (6)
39. French native's poor Roman neighbour initially seen at the top (6)
40. Fall of Nazis left Russian with no adversaries, at first (4)
41. New oak perhaps put under bottom of satellite dish (6)
42. Most of Canadian group is eating – go for Indian bread? (6)
43. Clergyman's starting to proselytize: At first Rhode Island, then Maine, Massachusetts… Connecticut, finally? (6)
45. Essential part in 9 across's language? (5)
47. Second time converting group of people? (4)
48. Female American welcomed (5)
49. Leaders of ancient Rome captured by possibly a Persian unit (5)
50. Maine produced cartoons (5)
51. Actor Jason cut out meat immediately (4)
55. Informally discuss beast of burden (3)
56. Deliverer of unopened containers for drinking (3, abbr.)
1 (Not really sorry.)