It appears that when some third-party Bluetooth headsets are paired with the iPhone and active (a phone call is in progress), Wi-Fi-based browsing in Safari is not possible.
A poster to Apple's Discussion boards, Rehan Ashroff, writes:
"This is what I am experiencing so far. Scenario 1: connected to WIFI; start phone call; audio source: bluetooth headset. Cannot browse Web using WIFI, pages dont load.
"Scenario 2: (connected to WIFI; start phone call) except this time I am using the built in speakerphone and not using a Bluetooth headset, and can surf the web using WIFI while on a call. [...] My headset is a Jabra BT250."
Another poster, hitherto, wrote:
"I have experienced the exact same problem described in this thread using iPhone Sony bluetooth headset. I also went into the Apple store and showed them the issue... they said 'don't use bluetooth on a call if you want to also use Wi-Fi."
It appears, however, that the Apple Bluetooth headset is immune to this issue, and will allow the user to browse pages in MobileSafari while the headset is actively engaged in a phone call.
As previously noted, the iPhone cannot access data (including Web browsing functionality) over EDGE while a phone call is active.