With the holidays upon us and Chinese plants working around the clock churning out Apple handsets (Foxbots should help automate assembly in the near future), no wonder analysts recently started seeing iPhone 5 inventory at Apple’s brick-and-mortar stores improving and at their highest level yet for AT&T, Verizon and Sprint customers. This week, availability of online orders on Apple’s web store also has improved as a result…

Recently, ordering an iPhone 5 via Apple’s US online store yielded a delivery estimate of 2-3 weeks.

This is from a week ago.

And this from yesterday.

As you can see, Apple now quotes a 2-week delivery estimate for the handset. This is valid for both the US and Canada web stores.

Note, however, that online orders remain limited to two per customer.

Of course, experienced shoppers who want the phone now can simply waltz inside their carrier’s retail outlet or one of the Apple stores in the hope of picking up an iPhone 5 right on the spot.

Another option is Apple’s online reservation system letting you place an order online between 10pm and 4am for in-store pickup the following day.

Though the iPhone 5 bottleneck appears no longer in the supply chain, Foxconn is still experiencing difficulties assembling the more complex product.

Its Chairman Terry Gou admitted in October that plants are “falling short of meeting the huge demand”. He previously described the iPhone as “the most difficult device” his workers have had to assemble.

But don’t open that champagne bottle yet.

As Apple launches the popular handset in the massive 1.33 billion people market of China this or next month and preps to unleash the next phase of the global roll-out, its supply chain could again face difficulties meeting high demand going into the holidays.

Don’t forget that Apple’s self-imposed promise entails launching the iPhone in a hundred countries on 240 carriers by year’s end.

Do you think that’s feasible?