Across
Forget it is either Edward or Kelly being a rat-catcher? (5,4)
Sad Parisian you dressed in bit of lady's underwear (3,2)
Tense nurse speaks about damn silly instructions for man taking tablets (3,12)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘about’) of ANDM, an anagram (‘silly’) of ‘damn’ in T (‘tense’) plus EN (enrolled ‘nurse’) plus COMMENTS (‘speaks’), with a cryptic definition.
Is in possession of one drug or another (4)
I haven't cracked this one yet — but Fifteensquared have:
A charade of HAS (‘is in possession of’) plus H (heroin, ‘one drug’), the definition being ‘another’ drug, hashish, a marijuana product.
Running a web browser, searching for wild animals (2,6)
Drink some beer, eating egg hard-boiled, perhaps (5,4)
African animal almost weed on Imogen's jacket (5)
Didn't stand by younger man who's a bit of an animal (5)
Fit female wearing a wonderful flip-flop in America (5-4)
First-class pilot receiving officer promotion and praise (8)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘receiving’) of CO (commanding ‘officer’) in ‘a’ plus CLADE ( Emil , WW11 Luftwaffe ‘pilot’). … but see russtoo @2 for a parsing which avoids the name unfamiliar to many (at the expense of using ACE in two adjacent answers).
I try welcoming bishop in a West African language (4)
Fancying that man wearing felt hose out dogging (3,2,3,5,2)
Manufacturer of pop, like one Jack drinks (5)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘drinks’) of AS (‘like’) plus I (‘one’, Roman numeral or personal pronoun) in OS (Ordinary Seaman, ‘Jack’), for one of the pop music bands so named (but not the soft drink – it is a brand name of the drink, not its manufacturer, and ‘pop’ generally refers to something carbonated; thus the definition is cryptic).
One bringing up issue that's arisen with mud wrestling (9)
Down
Hard time accepted by criminal up in nick (5)
I haven't cracked this one yet — but Fifteensquared have:
A reversal (‘up’ in a down light) of H (‘hard’) plus CTOH, an envelope (‘accepted by’) of T (‘time’) in CON (‘criminal’).
Word spoken by Caesar before child's game (7)
Cross thoroughfare with nothing covering area inside it (4)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘inside it’) of O (‘nothing’) plus (‘covering’) A (‘area’) in RD (road, ‘thoroughfare’).
Something penned by William Blake? (4)
500 homes tidy up mess, say (6,4)
I haven't cracked this one yet — but Fifteensquared have:
A charade of D (‘Roman numeral, ‘500’) plus In (home) plus IN (home, hence ‘homes’) plus GROOM (‘tidy up’).
Poets, we hear, making clangers? (10)
Fail removing odd bits of sacred drinking vessel (7)
I haven't cracked this one yet — but Fifteensquared have:
A charade of TANK (‘fail’) plus ‘s A c R e D ‘ ‘removing odd bits’.
Sports team with jerk in a danger to cricket? (9)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘with … in’) of TIC (‘jerk’) in PE (‘sports’) plus SIDE (‘team’).
Special note probing government's dishonesty and plots (10)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘probing’) of N (‘note’) in S (‘special’) plus TORY LIES (‘government’s dishonesty’).
Problem for wizard, this being the case at times (3,3,4)
Crazy chap, is it? Character resembling a football nut (9)
I haven't cracked this one yet — but Fifteensquared have:
A charade of PISTACHI, an anagram (‘crazy’) of ‘chap is it’; plus O (‘character resembling a football’).
Ancient writer understood Guardian readers (7)
You heard blow is consumed by teetotallers in American capital (7)
I haven't cracked this one yet — but Fifteensquared have:
An envelope (‘is consumed’) of U (‘you heard’) plus GUST (‘blow’) in AA (Alcoholics Anonymous, ‘teetotallers’), for the capital city of Maine.
Old G-man with a stutter is taken out (5)
I haven't cracked this one yet — but Fifteensquared have:
A charade of O (‘old’) plus F-FED (‘G-man with a stutter’). The definition is colloquial for killed.
Make black tea (4)
Amused expression inspired by 25 (2-2)
Type letters or click words in the clue