Can I replicate a database from SQL Server 2012 to SQL Server 2014 (with 2014 distributor)? I am planning to have database replication running from SQL Server 2012 (publisher) to SQL Server 2014 (both distributor and subscriber) -- pull replication.  

Has anyone done this type of cross-version replication and knows if there are any issues with it?

Thank you!
If you are using Transactional Replication then yes, this configuration is supported.

This is covered in Using Multiple Versions of SQL Server in a Replication Topology:


  For all types of replication, the Distributor version must be no
  earlier than the Publisher version. (Frequently, the Distributor is
  the same instance as the Publisher.)


Since your Distributor version is a later version than your Publisher version, you are good here.


  For transactional replication, a Subscriber to a transactional
  publication can be any version within two versions of the Publisher
  version. For example, a SQL Server 2000 Publisher can have SQL Server
  2008 Subscribers, and a SQL Server 2008 Publisher can have SQL Server
  2000 Subscribers.


Since your Subscriber is within two versions of your Publisher version, you are good here.

However, this configuration is not supported if you are using Merge Replication since your Subscriber will be a later version than the Publisher:


  For merge replication, a Subscriber to a merge publication can be any
  version no later than the Publisher version.


If you have anymore questions, please let me know.  I hope this helps.