The Example schematic only has 100uF + 0.1uF + 1000pF across the rails.
Have you considered the "mF" may be a typo? In one place, the datasheet says
typically 0.1 mF to 1 uF. I wonder if they meant to type n, and accidentally hit m. Also, I copied the
u symbol out of the PDF, and it got printed as
m when it was pasted. Cut&Paste may be at fault here, it certainly seems to be used within TI's various datasheets.
Also, millifarads have come to be an almost unused unit. It's generally Farads -> microFarads -> (nanoFarads - somewhat uncommon) -> picoFarads.
Furthermore, looking at the TPA3111 Evaluation Kit is informative:
The device is bypassed with two 100uF electrolytics (along with 0.1uF and 1000pF ceramics).
Also, looking at similar parts from the same line is informative. The TPA3110 (15W vs TPA3111's 10W) merely says
a larger aluminum electrolytic capacitor of 220 uF or greater placed near the audio power amplifier is recommended. It's worth noting that the same datasheet's example schematics only use two 100uF caps for bypassing.
The same note as in the TPA3111 is present in the TPA3112 datasheet.
It's also worth noting that the TPA3110 and TPA3113 have identical "Power Supply Decoupling" paragraphs, despite the fact that one is half the power of the other (15W vs 6W), which further inclines me to think typo.
The 25W TPA3123 only recommends 470uF of bulk capacitance.
The 100W TAS5121 only recommends 1000uF.
Edit: We will see if it is a typo: "Below is what you submitted to email@example.com on Tuesday, July 26, 2011 at 04:13:23; E-mail: firstname.lastname@example.org Lit Number: SLOS618BB Part Number: TPA3111D1 Error Page No: 19 Error Description: Please see this thread: HUGE capacitor recommended in datasheet for Audio Amp"