Explanations

The puzzle celebrated the fourth month of the year; to whit April. There was a vague reference in each of the thematic clues to a well known group of four. However, these were to be solved by taking the fourth letter of each of the words. This would give the name of a Shakespeare play in each case, with the answer to be entered being one of the characters of the play. In final recognition of the month, and in particular of the day the puzzle was released, the character in each case was a Fool!

Across

1. STUPIDITY (ignorance) minus ST (forces good man out) replaced with C (cocaine) => CUPIDITY (desire)
2. TraCk plaYing claMorous numBer upsEtting PauL motIvating LenNon movEment => CYMBELINE => CLOTEN
3. RIMS (is Mr Smith) contained in LIE (deception) => CRIMSON (embarrassed)
4. MAST (post) containing SIR (gentleman held) reversed (read back) => TSARISM (dictatorship)
5. Initials (basically) Irritating Minute Arthropod Grown Older => IMAGO (&lit)
6. Anagram (making a mess of its ingredients) continued => UNNOTICED (in the shadows)
7. CUR (dog) + TAINCALLS (cats in all contests) => CURTAIN CALLS (final displays)
8. WasHerwoman cleAns sumMer falL elsE winTer => HAMLET => GRAVEDIGGERS
9. DI'S (girl's) + MAN (boy) + TLE (let out) => DISMANTLE (break)
10. RecOgnise BlyTon autHor's advEnturous chiLdren deaLing refOrm => OTHELLO => CLOWN
11. ENAM (pull hair back) + OUR (for us) => ENAMOUR (please)
12. TR (translation) + AC (power) + TOR (hill) => TRACTOR (&lit)
13. SAY (perhaps) containing (catching) FEL (most of cut=fell) => SAFELY (no worries)
14. RE (on) + HEARSE (expired transport) => REHEARSE (test)

Down

1. CY (ChemistrY disheartened) + C (college) + L (student) + I + C (start Counselling) => CYCLIC (regular)
2. PRIM (correct) + AL (cALl taking wings off) => PRIMAL (optimum)
3. D (guitar string) + IS + SO (thus) + LUTE (instrument) => DISSOLUTE (loose)
4. Anagram (wrong) two + nurses + get + it => TONGUE TWISTERS (difficult reports)
5. Contained in (constituents) middLE AS Topmost => LEAST (bottom)
6. PesTilence ridEr seeMed resPectable thrEe horSemen rotTen => (THE) TEMPEST => TRINCULO
7. O (round) + MA (mother) contained in NDISM (dreadful state of minds) => NOMADISM (tendency to move)
8. TIN (metal) + GIN (drink) contained in SGNETTLES (gentlest setting) => STINGING NETTLES (plant)
9. Anagram (sadly) no + cracker => CORNCRAKE (bird)
10. A + GEN (general) containing (holding) D (Germany) + E (East) + SS (special army group) => AGEDNESS (seniority)
11. RusHmore facEs sigNifying fouR greY polItical serVants => HENRY IV => FALSTAFF
12. DiaMond strAight forCes cluB expErt's hasTy resHuffle => MACBETH => PORTER
13. U (Unusually first) + NT (books) + RUE (suffering) => UNTRUE (fiction)
14. A + TOLL (ring) => ATOLL (rosy ring)