1 One should auger best of all, and want to get started… (5,2,3,3)
10 …and one might augur well, if told to be good. (7)
11 A parent is about to hold the winner at Actium. (7)
12 Following one of the things that make residue? (7)
13 The main turning point to one rhyming with squash. (7)
14 Standards set by junior officers. (7)
15 Dish that returns the title to the emperor. (7)
16 How some bad nails are not stored away. (7)
20 Jack-low combination, but you might need more than one shot with it. (7)
23 Just a tumble-down place of spiritual association. (7)
24 One aspect of Locarno pertains to a kind of luminous light. (7)
25 The band may carry the show, but it’s frequently changed. (7)
26 Sauce that could be taken by degrees in a tortilla. (7)
27 A flier that went to school? (It should take experience to make one.) (8,5)
 2 Proves a nuisance when her airs alter it. (7)
 3 Tom might be in a state, briefly, having the habit. (7)
 4 How one behaves in the evening? (7)
 5 An acute ache really shows up the head of the class! (7)
 6 Gets up to look around what we all were, and gets dressed. (7)
 7 It might be necessary to get a second-hand organ. (7)
 8 If the radio program drifts, it might be the direction of the speaker is wrong, getting this. (3,3,7)
 9 Fish stories might be, but mumps make it. (4,2,7)
17 Hospital patients might be so headed, as one makes an advance. (7)
18 Was the speech of the Spartans? (7)
19 What the fastest gunman gets to allow a tiny bit of water in the fall. (7)
20 Found and ate cold hash. (7)
21 Old Indian or French name for an animal. (7)
22 With such, is the up-keep criticized? (7)
Please see the Letters page for the explanation of the first part of clue 9 in the June 7 puzzle, No. 1588 (that is, if you were as stumped as we were).