How can I determine a .dylib's version info on OS X?

You can use otool (/usr/bin/otool) to see the names and version numbers of the shared libraries that a Mach-O object file uses.

MacPro:~ mdouma46$ otool -L /usr/lib/libssl.0.9.7.dylib 
/usr/lib/libssl.0.9.7.dylib:
  /usr/lib/libssl.0.9.7.dylib (compatibility version 0.9.7, current version 0.9.7)
  /usr/lib/libcrypto.0.9.7.dylib (compatibility version 0.9.7, current version 0.9.7)
  /usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current version 169.3.0)

MacPro:~ mdouma46$ otool -L /usr/lib/libssl.0.9.8.dylib 
/usr/lib/libssl.0.9.8.dylib:
  /usr/lib/libssl.0.9.8.dylib (compatibility version 0.9.8, current version 47.0.0)
  /usr/lib/libcrypto.0.9.8.dylib (compatibility version 0.9.8, current version 47.0.0)
  /usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current version 169.3.0)

MacPro:~ mdouma46$ otool -L /usr/lib/libgutenprint.2.dylib 
/usr/lib/libgutenprint.2.dylib:
  /usr/lib/libgutenprint.2.dylib (compatibility version 4.0.0, current version 4.0.0)
  /usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current version 111.0.0)
  /usr/lib/libgcc_s.1.dylib (compatibility version 1.0.0, current version 1.0.0)

MacPro:~ mdouma46$ otool -L /usr/lib/libcurl.4.dylib 
/usr/lib/libcurl.4.dylib:
  /usr/lib/libcurl.4.dylib (compatibility version 7.0.0, current version 7.0.0)
  /usr/lib/libssl.0.9.8.dylib (compatibility version 0.9.8, current version 47.0.0)
  /usr/lib/libcrypto.0.9.8.dylib (compatibility version 0.9.8, current version 47.0.0)
  /System/Library/Frameworks/LDAP.framework/Versions/A/LDAP (compatibility version 1.0.0, current version 2.4.0)
  /System/Library/Frameworks/Kerberos.framework/Versions/A/Kerberos (compatibility version 5.0.0, current version 6.0.0)
  /usr/lib/libz.1.dylib (compatibility version 1.0.0, current version 1.2.5)
  /usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current version 169.3.0)

It's not always perfect, but if you provide any specific cases you're trying to figure out, I could advise further.

Unfortunately, it appears that otool isn't part of the default install, but is available as part of the Command Line Tools module of the Xcode developer tools. There are 2 ways to acquire otool:

The first way is might be the easiest, but will require downloading the 1.5 GB worth of Xcode.app on top of the 100 MB of the Command Line Tools. The possible upside of this method is that may help automate the download and install of the Command line tools. The second way requires setting up a free Developer account (unless you already have a paid one) at https://developer.apple.com/programs/register/ (NOTE: option 1 may even require this, I'm not sure, as I'm already a paid member), then connect to https://developer.apple.com/downloads/ and download the appropriate Command Line Tools for Xcode from the list of downloads.

If you go the first route, get Xcode in the app store at https://itunes.apple.com/us/app/xcode/id497799835?ls=1&mt=12.