There is usually a 'built-in' filter inside your teapot. If you look inside your pot, you can observe a filter at the spout joint. This filter is also known in Chinese as the 'bee hive'. This filter is useful to prevent the tea leaves from exiting when you pour out your tea. The Japanese teapots sometime have a small metal mesh filter instead. Do keep your filters clean by washing out any tea leaves that is caught in the filter. Exercise some care as not to damage the filter if you are using tools to clean the filter.
The 1st pix shows a ball filter. There are also flat, unobtrusive filters in many teapots. I know many tea drinkers and tea shops use an additional mesh filter (handheld), when they brew their tea. They use this handheld filter prior to pouring out the tea into a pitcher before serving. This is to ensure that your served tea do not contain any tiny tea leaves that is not caught by the teapot filter. I personally do not use the handheld metal filter.
I was told that the Chinese teapot develop the use of beehive filters in the manufacture of the teapots only in the past 12-15 years ago. The older teapots do not have a built-in filter (see pix2). It is interesting that I found this teapot felt lighter for its size.
Almost all Chinese teapots (yes, even the very expensive ones) today are made from moulds. Teapot makers make moulds from a teapot and subsequent teapots are made from these moulds. Though you will expect that every production of a teapot production run will be identical in terms of size and shape, there will be small differences when you compare these teapots. This is because there are some hand-work done during the production stage. Spouts and handles are joined by hand. The overall teapot is also hand-finished. You can easily spot this handiwork when you are buying a teapot.....alignment of the handle or spout are some examples. Some teapot makers use a potter's wheel in the production stages, thus the concentric lines on the inside of the lid and teapot (pix 3&4).
I myself have bought a couple of teapots. I did buy a few teapots from Yunnan Sourcing especially the Da Hong Pao range (I will devote a blog entry on this). I have not bought any teapots for investment. I only buy teapots if they catches my eye.....and since I am a little clumsy(broke a couple already).....will not buy the expensive teapots.