Solution to 28A has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to answer, if not solved by 1 PM.
ACROSS
1 Part-time auditor at Southern University submits a bill ultimately... (6) CASUAL {CA}{S}{U}{A}{bilL}
4 ...working as stopgap (6) ACTING [DD]
10 Device used in the past vehicle with misgiving and hesitation (4,6) CARD READER {CAR}{DREAD}{ER}
11 Basically third son has material (6) TISSUE {Th..d}{ISSUE}
12 Abstain from tea as per advice? Perfect (8) TEETOTAL {(~tea)TEA}{TOTAL}
13 Hungry lady, out of work after constant stalking by people, church officials (9) CLERGYMEN {Lad{ERG}Y}<=>{C} and {MEN}
15 Discreet company in California at county border (5) CAGEY {CA}{GE}{c...rY}
16 Warns Cristiano and Ronaldo diving slyly in the front (5) CARDS Acrostic
18 These are used to log-in and take drastic measures to suppress news upfront (9) USERNAMES {MEASURES}* over {News}
22 These days, getting order one becomes blue (8) CERULEAN {CE}{RULE}{AN}
23 Infosys temporarily prevented usage (6) SYSTEM [T]
25 English dramatist takes chicken on Christmas (4,6) NOEL COWARD {COWARD}<=>{NOEL}
26 Ball gets bat's edge and drops basically (4) BEAD Acrostic
27 An alternative to her? Primarily it's terribly exciting in a bad way (6) EITHER {HER+Its+Te...y+Ex...g}*
28 Withdraw or lead, but not quietly (6) ?E?E?E (Addendum - RECEDE pRECEDE - See comments))
DOWN
1 Type of cable, cord that is cut in half having 1111 etched on left (7) COAXIAL {COrd}{A}{XI}{A}{L}
2 Descriptions on glasses (5) SPECS [DD]
3 Pseudoscience my chapel disseminates without pressure (7) ALCHEMY {MY+CHApEL}*
5 My optician finally provides a drug in counter for part of the eye (6) CORNEA {COR}{o...aN} and {A}{E}<=
6 Lover's in a marriage basically, or one troubled initially, acting (9) INAMORATA {IN}{A}{Ma...e}{OR}{A}{Tr...d}{A}
7 Explosive is unsophisticated, missing the core, made without cap (7) GRENADE {GReEN}{mADE}
8 Relatives get rest in brawl; Oh, they are relaxed (8-2-3) BROTHERS-IN-LAW {REST+IN+BRAWL+OH}*
17 Marine polyps, one born around first working day of the week (7) ANEMONE {A}{NE{MON}E}
21 Sit behind editor, facing the other side and dismiss (6) DEPOSE {POSE}<=>{ED<=}
24 Fighter bashed grabbing from the back with a weapon (5) SABRE [T<=]
Reference List
Southern = S, University = U, Hesitation = ER, Constant = C, Company = GE, These days = CE, Christmas = NOEL, Quietly = P, Pressure = P, My = COR, Drug = E, Acting = A, Born = NEE, European = E, Editor = ED