Mixed Code refers to a situation in which code, or sometimes data, of differing privileges share the same context. An adversary may be able to craft malicious code to compromise the confidentiality and/or integrity of differently trusted code/data, enabling exploitation of elevated permissions.
For Java PlugIn and Java WebStart, see Oracle's Mixing Signed and Unsigned Code guide.
For HTTPS, see Ivan Ristic's How to Render SSL Useless, particularly points "8 Mixed page content," "10 Using SSL for “important” bits" and "3 Mixing SSL and plain-text".