Neutral-ground bonding

The panels are wired correctly. There must only be one connection between neutral and ground in the main service panel.

If a subpanel has a bond, then it puts the neutral in parallel with the ground wire back to the main panel -- and this means current from normal loads (that normally the neutral would carry) will travel on ground paths back to the main panel. This includes bare ground wires, conduits, and metal housings. If someone were to touch anything grounded, they could be electrocuted.

This can also mean that the magnetic fields created in the hot and neutral don't cancel each other out, which can generate a lot of interference.

In the worst case, bad connections or other faults can cause a voltage difference between ground and neutral, causing a lot of very difficult to diagnose problems, and making it even more likely to be electrocuted by touching something grounded (anywhere in the house, from any panel).

In short: There must be only one bond between ground and neutral, and it goes in the main panel.

Differences in voltage

The differences in voltage between the two busses is fairly normal. It is likely caused by the transformer on the pole, or by a load in your house that is causing a voltage drop. For the latter you can try turning off circuits to see if it goes away, but for the former, you're pretty much SOL. That said, it's not a problem. Mains in North America is supposed to be 120V +/-5% (so 114 to 126V is acceptable).

The voltage from neutral-ground is also normal. Here is a decent (but technical) article on neutral-ground voltage. In short, it's caused by the fact that over any length of wire, you have some drop in voltage. Since no current flows in the ground wire, there is no drop there and thus you have a difference in voltage. Another source is induced current, which can be caused by wires going through magnetic fields, such as near motors.

In short, it doesn't sound like you have any problems.

The best I could do was to dig up a fine print note (FPN) in the National Electrical Code (NEC). In theory, there is no limit (as stated in other answers). In practice, the limit is when things stop working. In this FPN, the limit is 3-5%. In reality, the limit is around 1-2%.

NEC 2008

210.19 Conductors — Minimum Ampacity and Size.
(A) Branch Circuits Not More Than 600 Volts.
(1) General.
FPN No. 4: Conductors for branch circuits as defined in Article 100, sized to prevent a voltage drop exceeding 3 percent at the farthest outlet of power, heating, and lighting loads, or combinations of such loads, and where the maximum total voltage drop on both feeders and branch circuits to the farthest outlet does not exceed 5 percent, provide reasonable efficiency of operation. See FPN No. 2 of 215.2(A)(3) for voltage drop on feeder conductors.

This Fine Print Note (FPN) says that to provide "reasonable efficiency of operation", the voltage drop of the branch circuit to the furthest point should not exceed 3%. And that the total voltage drop, including the feeders should not exceed 5%.

120V * 3% = 3.6V
120V * 5% = 6V

Given this information. You should start to examine your wiring, if you measure anything near 3V neutral to ground.

_{Note: Fine print notes are informational only and are not enforceable as requirements of the National Electrical Code.}