I purchased new electrolytic capacitors in order to restore an old tube radio, and when I tested them with my capacitance meter I noticed that one them is having higher capacitance than it should. It's labeled as 22 mf / 450 V. but it's actual capacitance is 27.5 mf, would it cause any problem if the needed capacitance is only 20 mf ?
Power supply electrolytic capacitors often have a tolerance of +/-20% or even -20/+50% (I've seen -20/+80%). Usually a larger capacitance does no harm (as you might guess from the way the tolerances are specified).
Your capacitor measures +25% (assuming the meter is measuring it accurately), which may or may not be within tolerance, but normally a larger capacitance does no harm, within reason. A much smaller capacitance than nominal would be a much larger cause for concern.
Electrolytic caps I commonly work with are labeled with +40%/-10% tolerance on the capacitance. Since electrolytic caps decay over time, making them far above the spec to start with allows the unit to stay in tolerance for longer.
In general, if the capacitance value was critical, nobody would have used an electrolytic to begin with. It's imaginable that having too much capacitance could damage a precharge circuit, but at that capacitance level I'd be very surprised.
It's difficult to say without knowing the application, but electrolytics are not the highest quality capacitors available. They have the advantage of high capacitance in a given volume, and are typically used where bulk capacitance is needed and precision is not. Most likely it would be okay to use.
It depends where you put it. If it's for the PSU, don't put it in the first position after the rectifier: put it after the first resistor or choke. The rectifier will have specified limits on the capacitance that it sees. If it's for a cathode resistor bypass, don't worry about it.