The error message is not indicating that the public key is missing but rather that the signature is bad.
I too have same warning message, I have tried all solutions provided here, but nothing works.
The possible workaround is Install from tarball:
I am just copy & pasting commands here from above link.
Download the binary files for the desired release of MongoDB.
curl -O https://fastdl.mongodb.org/linux/mongodb-linux-x86_64-3.2.0.tgz
Extract the files from the downloaded archive.
tar -zxvf mongodb-linux-x86_64-3.2.0.tgz
Copy the extracted archive to the target directory.
mkdir -p mongodb
cp -R -n mongodb-linux-x86_64-3.2.0/ mongodb
Don't just add keys from error messages. Only add keys you trust. Because any repository with this key, would be able to install any package without warning.
mongodb 3.0 has no warning messages,
sudo apt-key adv --keyserver hkp://keyserver.ubuntu.com:80 --recv 7F0CEB10
echo "deb http://repo.mongodb.org/apt/ubuntu trusty/mongodb-org/3.0 multiverse" | sudo tee /etc/apt/sources.list.d/mongodb-org-3.0.list
sudo apt-get update