A sick or injured pigeon with no obvious signs of injury might:

• Sit apart from the flock looking hunched up and depressed
• Fluff his feathers up and, perhaps, have difficulty keeping his eyes open
• Stay on the ground when the flock flies off or at dusk.
• Walk in circles.
• Throw seeds in the air.
• Totter backwards
• Have fits
• Use its wings to walk with (usually because its feet have become tied together)
• Be unable to fly
   

You can often catch a sick pigeon by scattering unsalted peanuts and throwing a soft coat over it when it comes near.

Be patient. Sometimes you only have one chance to catch it!