mysql replication goes out of sync for some tables
You could be suffering from what is known as data drift.
QUERIES
This can happen if there are queries that are unsafe for replication.
One of the more common types is running UPDATE or DELETE using LIMIT. Using LIMIT on DML can work just fine on a Master. On a Slave, the rows selected (and perhaps certain ORDER BY choices) may not be the same set being updated or deleted as the set on the Master. See the MySQL Documentation for a Comprehensive Description of Unsafe Statements that can affect MySQL Replication.
Baron Schwartz once dealt with this and had to refactor his query to get around this
The following hypothetical scenario illustrates one way to introduce data drift:
BINLOGS
Master

20 DB Connections writing changes (INSERTs,UPDATEs,DELETEs)
The I/O thread from a Slave has to serialize the SQL coming from the 20 DB Connections
The serializing of the queries into the binary logs may be in an order different from when each DB Connection executed its change.
sync_binlog set to 0 (default), which leaves the responsibility of flushing binlogs to disk in the hands of the OS

Slave

I/O Thread reads binlog events in the order the Master wrote them
SQL Thread executes binlog events in the order the Master wrote them

Observation
If binlogs are not flushed to Disk in a timely, predictable manner, any binlog events the Slave needs could easily be bypassed. This could cause data simply not exist on the Slave. Depending on the data recorded or not recorded, Replication's SQL Thread could break because of missing data or data that should be missing.
EPILOGUE
Not every Slave can be affected this way. Masters keep a list of all Slave I/O Threads and transmits binlog events to the Slave in order by ProcessID on the Master. I can see later slaves being victimized first.
If sync_binlog is indeed an issue, perhaps all Slaves have data drift and we just don't know of it yet.
The only way to tell is to download one of the following

mk-table-checksum
mk-table-sync

or

pt-table-checksum
pt-table-sync

and checksum everything on every Slave against the Master. You may find more data drift problems than you think. Just run the sync scripts to correct them.
CAVEAT
You suggested that network latency could be at issue. With binlogs not being flushed by the OS yet, any disconnect and reconnect of MySQL Replication due to latency or dropped packets is worth looking over as well. It could also be a major contributor to data drift.
Also to be noted is what network route the new Slave is communicating with back to the Master. If it is not the same route as the older Slaves (perhaps passing through a different switch, over public IP, etc.) needs to be investigated.