Yeh, that's exactly the problem. (and one of the PITA moments you get with Mint)
You have 2 options ..
1) edit your sources to say
Distribution: precise
Components: main
For both libreoffice PPA's (sources and binary)
instead of
Distribution: maya
Components: main
or
2) as you say, download the .debs and install
If you decide to want to go with option 1 .. post the output from:
ls -a /etc/apt/sources.list.d
and the if it exists, the contents of:
gedit /etc/apt/sources.list.d/libreoffice-ppa-maya.list
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