1 Take great care removing valves; firstly the top caps can be seized on resulting in the metal part detaching from the glass. If this happens you may be faced with a perfectly good valve but no easy way of getting at its top connection. If there is any of the top wire showing you may be able to resolder the cap back on but if there isn't you'll have to remove some of the glass pip. This can sometimes be done by a combination of filing away the glass with a sharp edged needle file or nibbling with a pair of sharp side cutters. When just enough wire appears carefully tin it and resolder the cap, if necessary using a very thin wire to extend what remains of the original wire. One can also use a small spring soldered to the inside of the valve cap and suitably terminated, perhaps silver paper, so it makes a pressure contact with the top pip. Superglue can be used to refit the metal cap to the glass but note that a soldering iron applied to superglue can produce gas that is close in toxicity to what was used in WWI. Make sure that the top clip isn't as tight as it used to be as a second attempt at repair may be impossible. Remove the spring steel clip if this is fitted.
2 The glass valve body may be loose where it goes into the bakelite base. This can be fixed with superglue. To get the valve out of its socket avoid pulling the glass, grip its base and use a flat screwdriver to help prise it out and when refitting hold the valve at its base if possible rather than the glass. You may find that a valve has lost its grey or red metal coating. In some cases it is essential that this is intact. If the valve has a slip-on metal screening tube it may be not too important but if it hasn't it may be impossible to stop an RF or IF stage from oscillating if the coating is compromised. If the exercise is to get the radio working properly one can use kitchen foil pressed over the valve to restore the screen. Note that one of the valve pins will be connected to the coating, usually a thin wire for this purpose will be found at the junction of the glass and bakelite.
3 If possible test the valves that come out of a set. This will aid fault finding. If this isn't possible you could try other methods. Substition of a known good valve is the obvious method, if one is available, once fault finding has commenced. The old method is to touch the top cap with a finger. Most stages will react to this and experience tells when all is well or not. Take care though, and check with data tables if you're not sure, because some older valves have their anode connection at the top not their grid. I remember once grasping a valve to pull it out when the set was switched on only to learn that for the all-metal catkin valves the outer metal IS the anode. It may be the outside of the anode but this has exactly same voltage as the inside. You will not wish to make the same mistake again!
4 Before any old set is seriously overhauled you must replace one specific component because it is ALWAYS faulty. This is the capacitor fitted between the audio amplifier and the output valve which will be leaky. As the input circuit impedance of the output valve is extremely high even a minute leak (10Mohms) through a capacitor will place a positive voltage on the control grid of the valve. This often has no other effect than to make the output valve run hot. In most sets the output valve will be operating in Class A and all the elevated grid voltage does is to push the valve operating point up its anode current curve. If the set has been used for some time in this state the valve emission may be poor. If one holds the valve to check its temperature before the new part has been fitted, skin may be left stuck to its glass and knuckles wrapped on the inside of the cabinet as one's hand is removed.
5 Most of the decoupling capacitors will be leaky but I'm not convinced that many of these will be worth changing. If an associated resistor has a high value, for instance in the AGC circuitry it may be beneficial to change a capacitor but otherwise, especially if the leak is small, don't bother. Electrolytics in the power supply should be changed if there is objectionable hum. Poor decoupling electrolytics may not have much effect other than to produce a bit of negative feedback. If overall gain is down a new one may be worthwhile at the output valve cathode.
6 Check resistors when cold. Don't worry unless the value is a lot out. For some reason "47" types are worst offenders. Often 47Kohms or 470Kohms will be miles out and should be replaced but all values are prone to failure. Often the one that comes out will be physically very large compared with a new one of the same wattage requirement. Although you may have a stock of old resistors always measure them first as they can fail or deteriorate whether they've been used or not.
7 Major components such as early HT electrolytics are often quite interesting objects and to preserve the look of a set's innards a new component (one hundredth of the size of the old one) can be put inside the old can (or cardboard box -if it's an ancient one).
8 If a valve in a series heater chain has developed a heater-cathode short or bad leak, the result may be a loud hum and not all the heaters may be lit. Some types of valve are now very scarce and a trick is to convert the heater chain to operate from DC. Rewire and put the offender at the "earthy" end of the chain if the leak is so bad that the heater current runs to ground via the cathode. Nowadays DC can be produced readily using silicon diodes and smoothing capacitors are tiny therefore take up minuimal space. You will need a ballast resisitor and perhaps a thermistor to provide the correct voltage and prevent a large inrush current. But this may be the only economic way of getting an old Bush AC/DC set back into service.
9 Mains energised speakers are a problem if they go open circuit or develop shorted turns. You can substitute a modern permanent magnet speaker with a separate HT choke (if you have one) or a ballast resisitor if you haven't. Don't forget that the matching transformer is probably bolted or riveted to the speaker so remove it before you throw it away.
10 If a rectifier valve has bitten the dust and a new one isn't to hand you can leave it in place (suitably disconnected) and fit a couple of silicon diodes. Use a couple of surge limiter resistors and adding a suitable negative co-efficient thermistor will delay the HT slightly. I'm not sure that applying HT too early is much of a real problem as a directly heated rectifier filament warms up a lot quicker than the indirect ones used in the rest of the valves anyway.
11 Once you start to deviate like this where will it stop? How about using high voltage VMOS transistors in place of the amplifier valves? In order to stop an EF50 oscillator being pulled by strong RF at 26MHz I once used an FET soldered to an old B9G valve base. It worked OK and was rock steady.