I should highlight from the very beginning that most of the features I am going to list are not that much improved by other vendors. But they at least have an option of providing other, fully supported storage engines that may overcome the problems in these features, while Oracle's trend to get rid of most engines but InnoDB makes MySQL users more seriously affected by any problems related to InnoDB.
- InnoDB's data compression
Classical InnoDB compression (row_format=compressed) has limited efficiency and does not get any attention from developers recently. Transparent page compression for InnoDB seems to be originally more like a proof of concept in MySQL that may not work well in production on commodity hardware and filesystems, and was not integrated with backup tools.
Bugs reported for this feature by MySQL Community do not get proper attention. DDL against partitioned tables and partition pruning do not work the way DBAs may expect. We still miss parallel processing for partitioned tables (even though proof of concept for parallel DDL and some kinds of SELECTs was ready and working 10 years ago). Lack of careful testing of partitioning integration with other features is also visible.
- InnoDB's FULLTEXT indexes
This feature appeared in MySQL 5.6, but 5 years later there are still all kinds of serious bugs in it, from wrong results to hangs, debug assertions and crashes. There are performance regressions and missing features comparing to MyISAM FULLTEXT indexes, and this makes the idea to use InnoDB for everything even more problematic. Current implementation is not designed to work with really large tables and result sets. DBAs should expect problems during routine maintenance activities, like ALTERing tables or dumps and restores when any table with InnoDB FULLTEXT index is involved.
- InnoDB's "online" DDL implementation
It is not really "online" in too many important practical cases and senses. Replication ignores LOCK=NONE and slave starts to apply "concurrent" DML only after commit, and this may lead to a huge replication lag. The entire table is often rebuilt (data are (re-)written) to often, in place or by creating a copy. One recent improvement in MySQL 8, "instant ADD COLUMN", was actually contributed by Community. The size of the "online log" (that is kept in memory and in temporary file) created per table altered or index created, depends on concurrent DML workload and is hard to predict. For most practical purposes good old pt-online-schema-change or gh-ost tool work better.
- InnoDB's persistent optimizer statistics
Automatic statistics recalculation does not work as expected, and to get proper statistics explicit ANALYZE TABLE calls are still needed. The implementation is complicated and introduced separate implicit transactions (in dirty reads mode) against statistics tables. Bugs in the implementation do not seem to get proper priority and are not fixed.
The Royal Pavilion of InnoDB in MySQL is beautiful from the outside (and somewhere inside), but is far from being completed, and some historical design decisions do not seem to be improved over years. We are lucky that it is still used and works nice for many current purposes, but there are too many dark corners and background threads there where even Oracle engineers rarely look and even less are improving them...