The "particular recording weaknesses" of the past were air, fire, and invaders. All still exist, but our recordings are generally more proofed against them than in the past. I tend to think that at a societal level, data preservation is on such a serious upward trajectory that categorization in order to begin to find meaning will be the greater challenge for future anthropologists.
Lots of data will also be lost to encryption - still stored on some tape, but with no one alive to remember who may have owned the keys, where they may be stored, and what formats everything is.
I would bet that a vast amount of the data stored today in S3 that will never be read again - either because it will be forgotten or actually deleted by Amazon (people stop paying their bills, companies go bankrupt).
Not to mention, we already know of things like the source code of 10-20 year old games that people still play having been entirely lost.
Those weren't intended to be kept around, but fires happen in cities, whether from a sacking or just back luck, and sometimes this would be hot enough to fire the clay.
In conclusion, the future will have just an enormous amount of coroplast political signs to fish out of landfills and decode, along with the ingredients on aluminium cans.