ACROSS
1 - A plain rightist, excited, is pernickety (13) - HAIRSPLITTING*
10 - Right hand reversed in painting: it is showing a joint problem (9) - ARTHRITIS {ART}{HR<-}{IT}{IS}
12 - Girl, escorted by students, is steady (5) - LEVEL {L{EVE}L}
13 - Swing! (9) - OSCILLATE [E]
14 - Such an angle is more than a right one (6) - OBTUSE [CD]
16 - Money made from dough (5) - BREAD [DD]
19 - Soup for the two containing a piece of radish (5) - BROTH {B{R}OTH}
20 - Footballer keeps doubly black thing found on the beach (6) - PEBBLE {PE{BB}LE}
25 - Priest who made Clem angry somehow (9) - CLERGYMAN*
26 - Advertisement for an aviator (5) - FLYER [DD]
27 - To fall behind the Spanish, on reflection, is lawful (5) - LEGAL {LE}{GAL}<-
28 - Order that at one time confined restless Indra (9) - ORDINANCE {O{INDRA*}NCE}
29 - Tempi rendered wrongly — that was decided in advance (13) - PREDETERMINED*
DOWN
2 - Bustle that an idler lacks (8) - ACTIVITY [CD]
3 - Pastoral wall painting changed at the top (5) - RURAL (-m+r)RURAL
4 - The magic medicine of Asterix! (6) - POTION [GK]
6 - Sudden flood following big shake, possibly (5,4) - TIDAL WAVE [CD]
7 - 98.6 (6) - NORMAL [CD]
8 - Urge the dogs beginning to hunt, with everyone ahead of ducks (6) - HALLOO {H}{ALL}{OO}
9 - Reportedly chews on pieces of information (5) - BYTES (~bites)
15 - Strained to get drugs distributed around capital of Liberia (9) - STRUGGLED {STRUGG{L}ED*}
17 - Put an end to a collector's item abroad (5,3) - STAMP OUT {STAMP} {OUT}
18 - Suspended animation for a regulation, say (8) - ABEYANCE [DD]
21 - Educated, lost head but made money (6) - EARNED lEARNED
22 - A device to measure notes in a particular order (5) - SCALE [DD]
23 - He has no choice in his vocation! (6) - BEGGAR [CD]
24 - More cynical insider, confused, loses heart (6) - SNIDER INSiDER*
26 - The enjoyment a soldier derives from primitive plants (5) - FUNGI {FUN}{GI}