Yes, mixing different fonts and typography is perfectly fine, so long as it is done tastefully. My approach to mixing different fonts is to give each font a purpose or a voice. The App would have a particular voice and the fonts would correspond to its personality. While things requiring input from the user would have a different font/voice. Using that as a guideline can help making things consistent and help you keep track of all the typography being used.
Check out this tutorial by Hoefler & Frere-Jones Four Techniques for Combining Typefaces
Another good example of it in use by Mailchimp.
