This sounds like it could be a hardware issue. I posted some questions so you can help clarify your situation, but the reason this happens could be because (in order from most likely to least likely):
If you're on a laptop, input from both the external mouse and internal touchpad can interfere with each other. If there are mulitple pointing devices connected, it also can cause strange behavior. Windows wasn't designed to accept competing input from two mouse pointing devices at the same time and be able to deal with each separately. So if something is accidentally bumping the touchpad or something else while you're trying to do something with the mouse, it might cause things like you describe to occur.
Your mouse button is starting to go. Because of their constant use, it's likely that they'll be the first to go due to wear. The contacts might be a bit finnicky and have become sensitive to nearly indetectible changes in pressure on the button. Different behavior while using the mouse in different ways might cause misclicks. The behavior might be beyond whatever debouncing the circuitry in the mouse is able to do.
The battery could be losing its charge. If it's a rechargeable battery, it's good to note that they do tend deteriorate over time. It should take a while before it causes an issue, but it can happen somewhat quickly if you tend to overcharge the battery. Even if it reports being fully charged, it still may not be providing enough power to maintain reliable communication with the computer.
Your wireless signal might be getting interference. Perhaps another device could be interfering with the wireless communication between the receiver and the mouse. Even if the device doesn't transmit, they still can emit EM interference and cause other devices to behave erratically. But if you have something else in the vicinity that transmits on the same frequency and by chance is being picked up by the wireless receiver, it might be confusing the two devices, similar to trying to use two different remote controls to control the same TV at once.
Your USB receiver for the mouse might be malfunctioning. If it gets unplugged, stored, transported, and replugged-in quite a bit, it's possible that it experienced wear to the point that it began malfunctioning. Storage in excessive heat or cold can also cause damage to electronic components (same goes with the mouse itself).
The USB port you're using could be faulty. This isn't an unheard of situation. Perhaps the USB root hub isn't working correctly because it's misconfigured. Checking the Device Manager can help you determine if this is a problem or not. Or, there could be a physical problem with the port itself. Since they get a ton of use, especially with devices like this, wear can occur and there might be a broken solder connection, or bent pin, that isn't connecting reliably and interrupting USB communication with the device.
Or, you could be having conflicts with other USB devices on your machine. This doesn't tend to be the issue these days, as operating systems these days are very good at managing USB devices. However, there's always potential for a rare case to happen that causes issues. Again, the Device Manager can report if there are any resource conflicts.
Best Answer
The buttons on a typical mouse are small mechanical switches, and like all mechanical devices, they do go bad. Even if the switch contacts are just dirty, it's unlikely that you would be able to clean them, because they are usually sealed units. I think you will have to replace the mouse. To find out for sure, try another mouse as a test.