Teapots can be a serious pain to clean. It's not just that it's hard to reach and scrub the entire interior of a teapot without a flexible brush; if that were the only problem, you could just soak it in hot soapy water, rinse it out and be done with it. The real problem is that teapots build up hard-to-clean calcium and lime deposits over time, and a long, hot soak won't be very effective at cleaning those stains. If you want to get your teapot as good as new, use this technique about once a month.
Fill the teapot with water. Pour in slightly more water than you normally do; this will ensure that the water level is higher than the calcium and lime deposits.
Pour in a little bit of white vinegar. About a third of a cup should do it, but there's no need to measure.
Bring the pot to a boil over high heat. Keep it at a full boil for ten minutes.
Remove the teapot from the heat and pour out the water and vinegar mixture. Allow the teapot to cool down enough for you to be able to clean it.
Soak the teapot in warm, soapy water. Submerge it to fill it with water and pour the water out of the spout. Do this several times. If you have a gentle bottle brush or kitchen scrubber with a long handle, you can use it to scrub as much of the inside as you can reach.
Rinse the teapot thoroughly and allow it to air dry. You should be able to see that the mineral deposits that were on the inside are gone.