One thing is quite obvious -- the contrast between "the True Church" and "the Church", 
each figuring thrice in the poem. (There's a link to the text in the original message.)
The "True Church" establishes its credentials in its first two mentions.
The main body of the poem is then devoted to the nature of "the Church" -- 
it gets three consecutive mentions.
The poem closes with describing the lot of "the True Church". 
A note of irony permeates the whole poem. 
Well, just a simple observation, FWIW. 

From: Chokh Raj <[log in to unmask]>
To: [log in to unmask]
Sent: Tuesday, November 1, 2011 9:22 AM
Subject: The Hippopotamus

Just consider Eliot's 'The Hippopotamus' and think whom exactly does it represent, 
the True Church or the False. 

Meanwhile some fun:

B. C. Southam suggests that Eliot saw a private joke here. He started as a banker's clerk
at Lloyd's in March 1917, "an event he signified here through an allusion to one of the Songs
in Sylvie and Bruno (1889), the novel by Lewis Carroll: `He thought he saw a Banker's Clerk
 / Descending from the bus: / He looked again, and found it was / A Hippopotamus: "If this 
should stay to dine," he said, / "There won't be much for us!"'" (A Guide to The Selected 
Poems of T. S. Eliot, 6th edn. [San Diego: Harcourt Brace, 1994]: 106).