The answers to the following clues will have something in common.

1. Someone has his sights on just you
2. Energetic exchange, as of opposing opinions
3. Thought and ideas do this
4. Math term used in fractions
5. Clash
6. To question the testimony of a witness
7. Child being difficult or bad-tempered
8. Additional information from a second source
9. In-flight aircraft concern
10. Type of sewing or embroidery
11. Triathlete's preparation
12. Pedestrian safety feature
13. Intersecting parallel lines used to shade a map
14. Cut-away view
15. Decision point
16. Deadly weapon
17. Pirate flag feature
18. Where NS intersects EW in the city
19. Track meet event
20. Angry outburst or a kinds of puzzles

Answers:

1. In the cross hairs
2. Cross fire
3. Cross your mind
4. Cross products
5. Cross swords
6. Cross-examine
7. Crosspatch
8. Cross-reference
9. Crosswinds
10. Cross-stitch
11. Cross-training
12. Crosswalk
13. Crosshatch
14. Cross section 
15. Crossroads
16. Crossbow
17. Crossbones
18. Cross street
19. Cross-country 
20. Cross words or crosswords