by Ken Stern

Solution: PEAR

The clues are cryptic clues, where the definition part gives the full answer and the wordplay part gives all but the first three letters. The enumeration is for the full answer, and as an aid the letters of the wordplay are given in alphabetical order for each group.

Clue Answer Wordplay (of rest of solution)
Stressed about zirconium and oxygen (9) SFORZANDO Zr (R) + and + O
Driving without error, very fast (10) BLISTERING st[e]ering
Blotchy shoulder muscle briefly comes back (7) MOTTLED delt (R)
Spin doctor to tee up, lacking power (9) PIROUETTE to tee up* - P
Oldest woman is a recordholder? (6) SLEEVE Eve (2)
Coo about ornate design (6) rococo coo*
Decree put a Bobbsey twin in cooler (9) ORDINANCE i(nan)ce
Error mixed up ode to unknown woman (4 3) JANE DOE E + ode*
Superficial interest in showy jewelry (8) dabbling bling (2)
OJ trial judge returning hideout for custodians (10) janitorial Ito + lair (R)
Type of cloud over "Big" region in California (6) CIRRUS Sur (R)
Three Senators ousted at once as Pell is mixed up in wages (6 4) TRIPLE PLAY P(Pell*)ay
Endless ceremony involved in resistance procedure (9) algorithm O(rit[e])hm
Golfer is old hand, partly with hesitation (6 6) arnold palmer old + palm + er
Dude, it's an alligator (6) CAIMAN man (2)
Within French island, rarest blood type is unknown (8) variable i(AB)le
Waiting, perhaps, to get $1000 for a fortress (10) STRONGHOLD on(G)hold
All over the place, weave a trigonometric curve (4 4) SINE WAVE weave*
Chang and Eng, for example, shattered wine stems (7 5) siamese twins wine stems*
Popular Salt 'n' Pepa song (4 2) push it hit (2)
Approved L.A. Law actress Susan to return (6) OKAYED Dey (R)
German duchy is finished (7) hanover over (2)
Expand our style with a high mound of hair in front (9) pompadour pad + our

The fact that three letters are omitted from each wordplay indicates that these three letters are to be used somehow, and the flavortext should clue that they are airport codes.

Solution Word Airport Code Airport location
SFORZANDO SFO San Francisco [Intl], CA, US
BLISTERING BLI Bellingham [Intl], WA, US
MOTTLED MOT Minot [Intl], ND, US
PIROUETTE PIR Pierre [Pierre Regional Airport], SD, US
rococo ROC Rochester [Greater Rochester Intl], NY, US
ORDINANCE ORD Chicago [Chicago O'Hare Intl], IL, US
JANE DOE JAN Jackson [Jackson-Evers Intl], MS, US
dabbling DAB Daytona Beach [Intl], FL, US
janitorial JAN Jackson [Jackson-Evers Intl], MS, US
CIRRUS CIR Cairo [Cairo Regional Airport], IL, US

Bristol/Johnson/Kingsport [Tri-Cities Regional Airport], TN, US

algorithm ALG Algiers [Houari Boumediene], DZ
arnold palmer ARN Stockholm [Arlanda], SE
CAIMAN CAI Cairo [Cairo Intl], EG
variable VAR Varna, BG
STRONGHOLD STR Stuttgart [Echterdingen], DE
SINE WAVE SIN Singapore [Changi Intl], SG
siamese twins SIA Xi An [Xiguan], CN
push it PUS Busan (Pusan) [Gimhae (Kimhae)], KR
OKAYED OKA Okinawa [Naha], Ryukyu Island, JP
hanover HAN Hanoi [Noibai Intl], VN
pompadour POM Port Moresby [Jacksons], PG

For each of the four groups, drawing the path on a map between the airports in the order indicated will produce the letters P, E, A and R in order, spelling out the answer PEAR.

The mention of "Great Circles" in the text might clue solvers to use the "Great Circle Mapper" (http://gc.kls2.com) to map the paths, as above, though any globe will do.