The entire poem is characterized by the principle of fragmentation with which modernist writers replaced the unified and chronological narratives of the past. To modernist writers and artists, fragmentation is the form of modernity as it reproduces the flux of human life, its fast pace and the multiple standpoints through which reality can be interpreted. Therefore, Eliot put together a long sequence of sketches which are apparently unrelated as far as time, setting and content are concerned. All the sections of the poem are characterized by abrupt transitions. In the first, for example, there are continuous geographical and seasonal shifts. In the third, we move from the contemporary urban setting of the "unreal city" to the ancient prophet Tiresias and then back again to the modern urban setting of London. Images of the city alternate with failed relationships through history.
You can find fragmentation throughout this poem, because it is both a theme and a technique. Eliot uses fragments because the land he describes is broken (fragmented). Therefore, look for and expect fragmentation throughout the poem.
However, if you want to identify the most notable uses of fragmentation, I'd suggest these:
1. The use of foreign languages. From the opening quotation in Latin and Greek, to bits of German, Sanskrit, etc. This is a world where people don't all speak the same language, and so don't understand each other.
2. Fragmented consciousness. This is both a fragmented identity and a fragmented sense of time. Look at the opening stanza, and you'll see other people's words drifting through the speaker's mind, and the speaker drifting from present to past.
3. Fragmentation of ordering systems. There are bits of different religions and spiritual practices here, like the Tarot. There are also clashing cultures and classes: pop songs blend with references to great works of literature. You can't tell which to listen to, and which to let guide you.