ITO World have a useful analysis tool comparing street-names recorded in OSM against those recorded in the OS Locator data set. http://www.itoworld.com/product/data/osm_analysis/main , but you may have to be registered and logged in to see it. They've done the analysis by local government area, giving a handy 'league table' of the completeness of each area (in terms of street-naming).
10 days ago, Gravesham was 142nd in the table, with 181 of its 1,133 street-names apparently missing. It was therefore rated 83.32% complete. As of today, it has risen to 76th position, with only 47 streets missing, and is now 95.23% complete.
It's been an interesting exercise resolving the discrepancies so far. Usually, the street-name is indeed missing from OSM, and in some cases this is because there is no street-sign on the ground (especially in rural areas - I've yet to find signs for Buckland Road, Wrangling Lane, Lockyers Hill, etc.). Discrepancies regarding apostrophes are extremely common (the ITO analysis separates these out as 'minor' errors), and for these I usually flag the other version as an alternative. Quite often, two street-signs for the same street will have different spellings, again often involving apostrophes, but also disagreeing about whether words are separate or joined together (e.g. Deneholm Road vs. Dene Holm Road).
Occasionally, the OS has clearly got it wrong, as in the three avenues in Northfleet which have been named '------ AVEUNE' in the Locator database, or the DRIVE which has become a DRLVE.