what you're describing sounds normal to me.
The following are some specs that I borrowed from
www.servocity.com describing the Futaba S3004 (standard) servo:
Control System: +Pulse Width Control 1520usec Neutral
Required Pulse: 3-5 Volt Peak to Peak Square Wave
Operating Voltage: 4.8-6.0 Volts
Operating Temperature Range: -20 to +60 Degree C
Operating Speed (4.8V): 0.23sec/60 degrees at no load
Operating Speed (6.0V): 0.19sec/60 degrees at no load
Stall Torque (4.8V): 44 oz/in. (3.2kg.cm)
Stall Torque (6.0V): 56.8 oz/in. (4.1kg.cm)
Operating Angle: 45 Deg. one side pulse traveling 400usec
360 Modifiable: Yes
Direction: Counter Clockwise/Pulse Traveling 1520-1900usec
Current Drain (4.8V): 7.2mA/idle
Current Drain (6.0V): 8mA/idle
Motor Type: 3 Pole Ferrite
Potentiometer Drive: Indirect Drive
Bearing Type: Single Ball Bearing
Gear Type: All Nylon Gears
Connector Wire Length: 12"
Dimensions: 1.6" x 0.8"x 1.4" (41 x 20 x 36mm)
Weight: 1.3oz. (37.2g)
Note that with a pulse width change of 400 uS (0.4mS) the servo will move 45 degrees. Most servos use a 1500uS neutral pulse width or thereabouts, so moving from 1.5 to 1.9 mS would move the servo 45 degrees one way, moving from 1.5mS to 1.1mS would move it 45 degrees the other way. That's pretty normal for typical servos.
The mechanical ability to travel 180 degrees between stops doesn't mean it's a 180 degree servo.