I'm migrating a WordPress site from one server to another, and the entire migration seems fine, except the sidebars aren't moving over properly. The obvious thing that comes to mind is a serialization issue with the MySQL migration, but I'm not making any changes to the database because the domain name isn't changing (or even the server paths for that matter). I'm literally just moving it from one box to another.
Rather than mess around trying to find the serialised data that got messed up, just use a tool to migrate environments and avoid messing up serialised data. WP Migrate DB is a good one that handles serialised data properly. The free version does a great job, as long as you don't have a huge database. The Pro version is the duck's nuts, well worth the money.
Broken sidebars on migration is indeed symptomatic of plain text replacement on serialized data...
In such situation I would try following steps:
examine environments, mismatch in encoding settings (WP and/or MySQL) can cause issues
examine process, personally I find tools that to end-to-end copying more robust than going through intermediary file
enable debug mode, broken data might manifest as errors from unexpected/bad inputs
manually compare source and target data after migration