The rule of thumb is that the more complex your theme is, the harder it will be to replace it with another. Themes should be only about styling your content, nothing more, and everything relating to content itself should be handled in plugins.
Unfortunately, most people think that all themes should come with everything and a kitchen sink, and therefor most themes are not doing styling only, and therefor are hard(er) to replace.
Regarding your current situation, it is hard to say anything concrete without actually understanding the nature of your problems, but yes if you have used in your content a theme specific shortcodes or other kinds of styling, you will need to adjust your content to play nice with a new theme.