When setting up a new BGP peering, you may want to test if your peering partner uses the correct MD5 password without bringing up your side of the session.
For this the tcpdump option -M can be used to supply the MD5 password when sniffing the traffic of the new peer:

tcpdump -ni eth0 -M MyBgPMd5PaSsWoRd tcp port 179

tcpdump will then verify the MD5 signature for every packet where it finds a MD5 signature TCP option as specified in RFC2385.
In the output you will see md5valid for packets where your password matches the MD5 signature or md5invalid for packets where your password does not match the MD5 signature.
If you see neither md5valid nor md5invalid then the peer did not configure any MD5 BGP password.

If you want to check for mismatching MD5 passwords after you bring up the BGP session, just look into the kernel log. Linux reports invalid MD5 TCP signatures like this:

MD5 Hash failed for (1.2.3.4, 56789)->(1.2.3.5, 179)