The fact that the access points share the same SSID does not alleviate problems of cross-talk and synchronization.
There are two types of "interference". I will term them "managed interference" and "unmanaged interference" for the purposes of this discussion.
Managed interference is the "good" kind of interference. This is where all the WiFi devices in the overlapping area are speaking a protocol that allows them to cooperatively share the available spectrum, even if they're on the same channel. You can think of this in terms of a highway: a managed interference on a highway is where someone puts on their turn signal indicating they'd like to get in front of you, so you let off the gas and allow them to get into your lane. The flow of traffic is only minimally impacted and now you're both in the same lane.
Unmanaged interference is the "bad" kind of interference. This is what causes severe problems with WiFi networks. It is distinguished from managed interference because at least one source of radio frequency emissions on a WiFi spectrum band is sending its interference without coordinating with WiFi devices that are also using that band. You can think of this in terms of traffic as a car that's spinning out of control and slams into you from the side, or a truck that lost its brakes and can't stop. Unmanaged interference could also be, say, an airplane trying to land on the highway. More than likely, unmanaged interference causes major problems such as crashes (lost data) and blockage of the road for an extended period (in the highway analogy, probably hours; in the WiFi world, probably milliseconds -- but a few milliseconds in WiFi time is a lifetime).
Unmanaged interference can further be divided into two kinds: unmanaged interference originating from other WiFi devices that, for some reason, are not cooperating with you to share the bandwidth; and interference originating from non-WiFi devices that just happen to be generating electromagnetic energy at the same frequency as WiFi uses.
An example of managed interference would be several devices operating on compatible protocols (e.g. RTS/CTS) where all the devices are within mutual range of each other.
An example of unmanaged WiFi interference would be several devices which may or may not operate on compatible cooperative protocols, or where one or more of the devices is completely out of range of one or more other devices on the same channel.
With multiple APs with overlapping or slightly overlapping ranges, you will very commonly have a situation like the one depicted in this article's picture:
The basic idea is that
S1 (say, a laptop user) can tell
S2 that it's transmitting to
R1 and vice versa, which causes
S2 not to talk over one another; but since
R1 is not in range of
R2, they can't work together so that
R1 will wait to transmit to
S2 is transmitting. This is an example of unmanaged interference, even though all devices involved are WiFi devices.
You can visualize this in the following way: you are trying to listen to someone talk through headphones you're wearing, while someone is talking to you face to face. You have two "transmitters" sending you information on the "same frequency band" (they are both speaking a language you understand, at about the same volume to your ears). But since the person speaking to you face to face can't hear your headphones, they don't know that you are already listening to somebody (assume that the person talking can't see your headphones; maybe you have them hidden underneath a hood or cap). They create interference for you because they aren't aware that they're talking over one another.
Examples of unmanaged interference from non-WiFi devices would include Bluetooth devices; cordless phones; poorly constructed electrical motors; vacuum cleaners; microwave ovens; and so on.
Your goal in WiFi network design should be to avoid all unmanaged interference whenever possible. Managed interference is usually tolerable in small amounts.
Obviously, you can't avoid some sources of unmanaged interference, such as cosmic rays from space, which occasionally contain electromagnetic emissions within the WiFi spectrum. But you should be able to control unmanaged interference from WiFi devices.
To avoid the exposed node problem, you can configure each access point to broadcast on a different frequency band (channel), which means that even if the different nodes are communicating with each other at the same time, and even if they can't all see each other, you will not get unmanaged interference between them. Interference, by definition, has to occur on the same frequency band (the same channel). If it's on a different channel then it isn't interference at all.
So if you are positive that all of your nodes are cooperating at all times using RTS/CTS or 802.11n fair scheduling, that's fine. But it takes a lot of effort to determine that everything will always be within range sufficiently that they can use the WiFi standard protocols to only create managed interference, which does not reduce bandwidth or cause long dropouts nearly as badly as unmanaged interference does.
What does the client do when both APs are on the same channel?
See above. In the best case, collision will be minimized/avoided by cooperative protocols that are designed to allow some degree of cooperation on the same channel. In the worst case, collision will occur very frequently if the devices can't all "hear" each other (including the access points and all the nodes accessing each access point). Remember, the transmissions have to go both ways; from the client to the access point, and the reverse direction.
What kind of errors can I expect?
If you have large amounts of "managed" interference, your bandwidth will decrease and latency will gradually increase the more interference you have. It won't drop right off a cliff; it will just get slower and slower the more devices you have connected. This is like cramming a lot of cars into a highway, but where each driver is in control of their vehicle and all of them are obeying the laws of the road. You end up slowing down traffic because of all the overhead of the protocol (signalling, braking to merge, etc.), and nobody gets to their destination as fast as they'd like.
If you have large amounts of "unmanaged" interference, including from WiFi devices that can't cooperate together due to range or protocol errors, your bandwidth and latency will fall off a cliff (it will be pretty unusable, in other words). This may be 100% of the time, 50% of the time, or only a small fraction of the time. But whenever you get unmanaged interference, it will cause very noticeable decreases in bandwidth, or may cause you to completely lose your wireless connection for several seconds (or up to a few minutes depending on the source and strength of the interference).
One last comment, regarding a reason why all of this might not be necessary.
On a sheet of paper, draw all of your wireless access points as a dot. Now draw a circle around each dot to represent the range of the WAP. Now, imagine that there is a client connected to that WAP at every possible point within that circle (well, more relevantly, on the edges of the circle -- along the circumference). Then, draw a circle around each client representing the range of that client.
If you were to actually complete this exercise, and you found that:
All clients connected to any given WAP are all within the range of all the other clients connected to that WAP.
No two WAPs have overlapping range at all.
No pair of clients connected to different WAPs are within range of each other.
In this situation, you should not have any "unmanaged WiFi interference". You will get managed interference between the clients connected to each WAP, and you will get unmanaged interference from the external environment (non-WiFi sources), but you won't get unmanaged WiFi interference, which is good. In this particular case, it is safe to set all the WAPs to the same channel.