1 Cathedral returns warm air, a madness (10)
warM AIR A MADNEss backwards is the ENDA MARIAM cathedral in Asmara, Eritrea.
2 All-salad cave mixes up historical house (12)
CASA DE LA VALL is a historical house in Andorra la Vella, Andorra (all salad cave rearranged).
3 Endless tomato sauce with flavourant vowels gives Casbah mosque (9)
As found by @JR_M, KETCHAOUA is a mosque in Algiers, Algeria. (Ketchup - up plus vowels in flavourant). Thanks, @JR_M!
4 Dirk C.O. Rosalyn backed off a monolith (7)
dirK CO ROSAlyn reverses is ASO ROCK, an outcropping just outside Abuja, Nigeria.
5 Sequel masker scrambles city plaza (12)
MESKEL SQUARE, the city centre of Addis Ababa, Ethiopia (sequel masker rearranged).
6 Spanish Diego's apple is exhibition complex (17)
MANZANA DE LA RIVERA is an exhibition complex in Asuncion, Paraguay. (Apple in Spanish is MANZANA, and it belongs to Diego RIVERA, a famous Mexican painter. So it is Rivera’s Apple => Apple of Rivera in Spanish).
7 Guitarist Steve and South American capital make writer's residence (7)
VAILIMA, the last home of Robert Louis Stevenson, is just south of Apia, Samoa. (Guitarist Steve VAI + LIMA, Peru).
8 Formula 1 location confused D analysis (9)
YAS ISLAND, in Abu Dhabi, UAE is the site of the F1 Etihad Airways Abu Dhabi Grand Prix (D analysis rearranged).
9 Fortification scales out incoherently (9)
@Dr Xorile found that OSU CASTLE, near Accra, Ghana is a fortification (scales out, rearranged). Thanks, @Dr Xorile!
10 Large bird with recognised safety professional inside small bird become wildlife reserve (10)
LEMURS PARK is a wildlife reserve in Antananarivo, Madagascar. (Large bird EMU, recognized safety professional RSP, small bird LARK => L + EMU + RSP + ARK).
11 Mameluk at an upside-down observation tower (7)
mamELUK AT An backwards yields ATAKULE, a communications tower in Ankara, Turkey.
12 Tall structure shuffles tiebreaker two (13)
BAITEREK TOWER is a tall structure in Astana, Kazakhstan (tiebreaker two rearranged).
13 Archaeological site backs peanut I ejected (6)
PeaNUT I EJected backwards yields JEITUN, an archaeological site north of Ashgabat, Turkmenistan.
14 Laminated mac rearranges Levantine ruins (12)
AMMAN CITADEL, in Amman, Jordan (Laminated Mac rearranged).
15 Boleyn Zappa residence is biographical museum (14)
This is the ANNE FRANK HOUSE in Amsterdam, The Netherlands. (Anne Boleyn + Frank Zappa + (house = residence) )
16 Ancient citadel is confounded ??? pro (???)
I think the clue should be Ancient citadel is confounded social pro (9). This leads to ACROPOLIS, the famous ancient citadel in Athens, Greece. (Social pro rearranged).
Looks like the common theme is
Tourist attractions in capital cities starting with A!