An unnamed Sharp executive has allegedly said at a press briefing held in Osaka that the company is producing "adequate volumes" of those 4" IPS displays. According to an estimate by an analyst, Sharp is capable of producing about 6 million displays per month, which is almost on par with one of Apple's other screen suppliers - Japan Display, the production capabilities of which are estimated at 8 million. In addition, Apple is also using screens from LG Display, so a shortage of displays isn't very likely.
Still, no one can deny the fact that if you try to order an iPhone 5 from Apple's online store right now, you'll be warned that the device will ship in about 3-4 weeks, which is quite a lot of time. Are the factories building the phone responsible for the delays? Has Apple favored the retail stores as far as stock goes? No one currently knows, but hopefully those shipping times will soon get back to normal.