I am considering setting up a second router as an access point. The routers will broadcast on different channels. Will this cause any problems, e.g. a non-continuous connection?
Assuming you plan to connect the two routers with an Ethernet cable (LAN-to-LAN), that is the correct way to do it. The channels should be different. The SSID, encryption mode, and keys should be the same. Make sure to disable DHCP in the new router and don't use its Internet/WAN connection.
My experience tells me that connection will not be lost, and that some devices, like the iPad and iPhone, switch over quickly to the best WAP.
However, some devices, while not loosing connection, are very reluctant to switch WAP. Both my Samsung Galaxy S2 and especially my VAIO laptop are such.
The VAIO can sit 15m from the WAP it first connected to and 1m from the other WAP, and still continually ignore the closest one, resulting in clearly inferior signal.
Bottom line: two WAPs will not hurt any devices, but it will only help some.