Counters in C* have a complex internal representation that avoids most (but not all) problems of counting things in a leaderless distributed system. I like to think of them as sharded counters. A counter consists of a number of sub-counters identified by host ID and a version number. The host that receives the counter operation increments only its own sub-counter, and also increments the version. It then replicates its whole counter state to the other replicas, which merge it with their states. When the counter is read the node handling the read operation determines the counter value by summing up the total of the counts from each host.
On each node a counter increment is just like everything else in Cassandra, just a write. The increment is written to the memtable, and the local value is determined at read time by merging all of the increments from the memtable and all SSTables.
I hope that explanation helps you believe me when I say that you don't have to worry about incrementing counters faster than Cassandra can handle. Since each node keeps its own counter, and never replicates increment operations, there is no possibility of counts getting lost by race conditions like a read-modify-write scenario would introduce. If Cassandra accepts the write, your're pretty much guaranteed that it will count.
What you're not guaranteed, though, is that the count will appear correct at all times unless. If an increment is written to one node but the counter value read from another just after, there is not guarantee that the increment has been replicated, and you also have to consider what would happen during a network partition. This more or less the same with any write in Cassandra, it's in its eventually consistent nature, and it depends on which consistency levels you used for the operations.
There is also the possibility of a lost acknowledgement. If you do an increment and loose the connection to Cassandra before you can get the response back you can't know whether or not your write got though. And when you get the connection back you can't tell either, since you don't know what the count was before you incremented. This is an inherent problem with systems that choose availability over consistency, and the price you pay for many of the other benefits.
Finally, the issue of rapid remove, increment, removes are real, and something you should avoid. The problem is that the increment operation will essentially resurrect the column, and if these operations come close enough to each other they might get the same timestamp. Cassandra is strictly last-write-wins and determines last based on the timestamp of the operation. If two operations have the same time stamp, the "greater" one wins, which means the one which sorts after in a strict byte order. It's real, but I wouldn't worry too much about it unless you're doing very rapid writes and deletes to the same value (which is probably a fault in your data model).
Here's a good guide to the internals of Cassandra's counters: http://www.datastax.com/wp-content/uploads/2011/07/cassandra_sf_counters.pdf