MySQL officially only supports replication to the next higher version (although it will work for 5.7.13+), see Replication Compatibility Between MySQL Versions:
MySQL supports replication from one release series to the next higher release series. For example, you can replicate from a master running MySQL 5.5 to a slave running MySQL 5.6, from a master running MySQL 5.6 to a slave running MySQL 5.7, and so on.
However, you may encounter difficulties when replicating from an older master to a newer slave if the master uses statements or relies on behavior no longer supported in the version of MySQL used on the slave.
By default, replication will stop if an error occurs, and you have to restart it (after fixing the error). If you use the --slave-skip-errors=all-option however, it will skip these errors:
Normally, replication stops when an error occurs on the slave, which gives you the opportunity to resolve the inconsistency in the data manually. This option causes the slave SQL thread to continue replication when a statement returns any of the errors listed in the option value.
Do not use this option unless you fully understand why you are getting errors. If there are no bugs in your replication setup and client programs, and no bugs in MySQL itself, an error that stops replication should never occur. Indiscriminate use of this option results in slaves becoming hopelessly out of synchrony with the master, with you having no idea why this has occurred.
MySQL 5.5. and 5.7. will actually behave differently for a lot of statements, so enabling this option in this scenario will require even more care.
Without seeing your actual table create-statement, it is unclear what exactly caused that problem and how to fix it (or if it is possible), but you should especially check your configuration settings. MySQL 5.7. enables strict mode by default, so a usual suspect for incompatibilites is e.g. a zero default value for date/timestamp-columns like default '0000-00-00' (either explicit or implicit), which is not allowed anymore, see no_zero_date.
Even if you seem to not be too keen about 100% replication (which can snowball very fast, but that is up to you to evaluate for your scenario), resetting your slave (after fixing e.g. the configuration settings) at least once is probably the easiest solution, as there might have been other things you may have missed, and, if executed without errors, will also doublecheck if your tables and data up to that point are compatible with your 5.7-slave now.
--slave-skip-errors-option (or did you maybe restart it manually after such an error occured that stopped the slave)? - Solarflare