1)  The dynamics of that fateful dialogue between Achilles and Patroklos, lines 36-100:

--Achilles, by sending Patroklos into battle with his Myrmidons but without himself, modifies his position yet again (having twice modified it in Book IX after hearing his companions' speeches). Why can't he simply captitulate (lines 60-63)? I argued that he now can't go back on his word (even his already-thrice-modified word) because to do so would render meaningless the deaths of all those men who have already been lost because of Achilles's refusal to fight. You may have an alternative (or supplementary) explanation.
--Patroklos proposes to go into battle as Achilles, to fight for Achilles's honor: this act of surrogacy lends special interest both to his actions on the field (they acquire additional symbolism) and to his attitude (I suggested that Patroklos himself begins to think that he is Achilles, thus ignoring Achilles's own words of warning to him at 87-94).
--About those words of warning: why might a god "crush" Patroklos for winning glory against the Trojans before Achilles is ready to join the battle himself? Why would Achilles be aware of such a motive?

2)  During his climactic Book 16 aristeia, Patroklos kills Sarpedon. This death has particularly strong symbolic aspects: partly because, as noted above, Patroklos acts here as a surrogate for Achilles; partly because of the symbolic polyvalence of Sarpedon himself. Remember, Sarpedon:
      (a) has an immortal parent (in fact, the very immortal parent that Achilles lacks): see esp. lines 666-676;
      (b) dies far from home fighting another man's war (V: 478-484);
      (c) is prime spokeman for the heroic (kleos-centered) code (XII: 310-328); and
      (d) leaves behind a wife and small child (V: 684-88)
Try cross-referencing these qualities with the main concerns of the two opposing heroes, Achilles and Hektor. How does the poem work out some of its central philosophical questions through the duel of Sarpedon and Patroklos?

By the way, note how the Lykians and others on the Trojan side (including Hektor) are rallied to fight harder for Sarpedon's sake (lines 548-553): another intimation of what people really fight for, when the chips are down (and thus, by extension, a premonition of what will make Achilles fight again).

3) There's a wonderful example of a Homeric simile at lines 384-393. Be sure to note the sheer pace of the passge, generated by Homer's words and imagery. Aside from that, its vehicle (invented image to which the Trojan horses are compared) is interesting: what two sides of life are depicted here that don't usually appear in the action of the Iliad?

4) Perhaps most dramatically, Book 16 sees Patroklos's death at the hands of Hektor. Some noteworthy aspects of that encounter (you can tease out their implications for yourself) are:
      -- Patroklos's overstepping the bounds set him by first Achilles (see above), then Apollo (lines 707-709), effectively dooming himself; contrast his conduct here with Diomedes's in Book 5.
      -- Apollo's direct onslaught on Patroklos (lines 788-94): this is the only time in the Iliad that a god intervenes directly, physically, to kill a human being (contrast the deception Athene practises on Hektor in Book 22). How do you make sense of this shocking intervention?
      -- Achilles' helmet hits the dust for the first time (lines 793-99). Symbolism?
      -- Hektor's vaunting over Patroklos's dying body: note that at 838-842, Hektor has it exactly wrong (I would add, 'as usual'). What do you think motivates his assumption?
      -- What does Patroklos's reply (lines 844-854) accomplish, in terms of (a) diminishing the kleos-value of his death for Hektor; (b) providing an antecedent type-scene for Hektor's similar speech in Book 22? What does Hektor's reply to Patroklos reveal about the character of Hektor, and how does it deepen our reading of Achilles's reply to Hektor in the parallel Book 22 scene?