There are four key parts in the 1502 that make repair difficult.
The original sampling gate (CR1732, Tek 152-0631-00) is no longer available, but Avago RF Schottky barrier diodes in the SOT series pair package (HSMS-2822, HSMS-282C) are a close substitute. These sampling bridges are so small and light that soldering them in place can be a frustrating experience.
The leads are plated steel and if the soldering iron has a magnetic tip (e.g, many Weller models with temperature control), this can cause the gate to be attracted to the iron. Even with a non-magnetic iron such as a small 15-watt Antex, the surface tension of the solder is enough to cause the gate to "float" away from its intended mounting location when the iron is removed from the molten solder joint. A special "hold-down" device can be made to hold the bridge in place and was described in a Wizard's Workshop article.
The first pulse shaping TD (CR1609, Tek 152-0140-01, 10 mA, 8 pF) was a fairly common TD and there are Russian substitutes available. The primary fast pulse TD (CR1703, Tek 152-0489-00, 21 mA, 1.5 pF) is simply no longer available. The closest Russian replacement is GI308E, it requires soldering to the original heatsink.
Replacement of the pulse generator might be done with Analog Devices ADCMP580. An interesting circuit can be found in Starecki and Misiaszek's paper, Low cost programmable pulse generator with very short rise/fall time.
There appears to have been an optional "static suppressor" in a BNC M-F package, Tek 011-0132-00, used to protect the sampler and TD. It's pretty obscure. The BNC connector on later 1502s contained an internal shorting bar that shorted the center conductor to the shell with no mating connector installed. In use, it was to short out the connecting cable so that any static on the line would be discharged before opening up the BNC connector to the internals of the TDR. Often, this shorting bar would break off, rendering the connector unable to discharge a cable to be connected. Replacing this BNC connector (or any front-panel component, for that matter) is a laborious process involving resealing the front panel for waterproofing.
The original 1502 and 1503 were the first Tektronix instruments to be fully waterproof (with the X-Y Module installed) such that it could actually be operated while submerged to a shallow depth. The front panel sealing is a very involved process utilizing several different silicone (grease and RTV) products to do the job. Tektronix produced a separate instruction manual specifically for waterproofing details of the 1500-series.
The other common failure is the battery. The power supply was designed to protect both the instrument and the battery from abuse, so any failure will cause the power supply to latch up (via Q6547/Q6549) and the unit will appear dead. The pack is rebuildable with NiCd battery cells. To operate without a battery in place use a 200 to 270 Ω / 10 W power resistor in parallel with a 2200 μF cap (> 25 V); this will fool the power supply protection circuit into thinking that it's charging a valid battery. The current drawn from the batteries is approx. 200 mA. Original batteries can be replaced by e.g. AA NiMH batteries with 2000 mAh for similar operating time.
Another common failure is a defective DISTANCE dial – operators expect the numerical readout of this dial to go from zero to 999 and it is not designed to do that. Often, the internal plastic stops get broken from operators forcing the dial past its intended stop, rendering the part useless.