Use the same citric acid cleaning procedures to clean tub interiors as outlined for dishwashers. Doing so removes mineral deposits, lime, and soap buildups that affect the pump operation.
If you have rust stains inside the tub, try a professionally installed plastic tub liner before considering replacement. Temporary patch-ups on small nicks in the porcelain where rusting occurs can be made with a dab or two of enamel paint or clear nail polish -- but these are very temporary solutions, at best. A better solution is a porcelain repair kit made for bathtubs, available at your local hardware store. It lasts longer, but not forever.
If your water outlet hose drains into a laundry basin rather than a stand pipe, cover the end with an old nylon stocking. Doing so collects 95 percent of all lint that otherwise would go into your sink's drain line. The nylon stocking filter also reduces splashing when the washer empties into the sink. When the stocking fills with lint, remove and replace it.
If your cold water is running slowly, turn off the water inlet valves, remove water hoses, and clean the small screen filters, which are probably clogged with mineral buildup and small debris. The fine mesh filters are usually at either end of the hose or on the back of the washing machine's water inlet port. If debris gets past these screen filters, it can damage the pump and lead to a costly repair.
Also consider switching from rubber water inlet hoses to long-lasting braided stainless steel hoses. They cost a little more, but both are good insurance against flooding caused by hose failure.