Esther is unique in that it is the only canonical book which does not explicitly mention God. The author's silence regarding God's involvement in the story is perhaps a suitably ironic play on the importance of Esther's hidden nationality. Regardless, there are many interesting points which can be drawn from this.
How should a pastor preach on Esther, and what implications does the answer to this question have to preaching in general? Some pastors I have listened to take the "commentary" approach to Scripture: they select a few chapters or verses for the sermon, examine those verses alone - perhaps recalling a few points made in last week's sermon - make a few practical applications, and then pick up next week's sermon at the point in the book at which the sermon finished. Not that there's anything necessarily wrong with this, but if one were to apply this to Esther, God wouldn't be mentioned in the church for several months.
Then there are canonical implications, of course. The reason it wouldn't be anachronistic for a pastor to mention God in a sermon on Esther is because the pastor recognizes Esther is God-breathed. God has a purpose for having revealed what He did, and that we have a canon from which we can draw universal truths about God as a recourse to discovering in what way God was involved in the events specifically recorded in Esther bespeaks of the success of biblical and systematic theologies as organizing principles of Scripture.
To take a biblical theological approach, for example, one might compare and contrast Queen Vashti and Esther to each other and, respectively, to cursed woman and ideal woman (cf. Genesis 1-3; cf. James Hamilton Jr. in God's Glory in Salvation Through Judgment, pgs. 321-322). There are also overt linguistic and thematic parallels between the Esther and Joseph narratives. Here are the few I found in my study:
Esther 1:3, 5, 9, 2:18, 5:4, 8, 9:17ff.; Genesis 40:20, 43:16ff. (feast motif)
Esther 1:12, 2:3, 21-23, 4:4-5, 6:2, 14, 7:9; Genesis 40:1ff., 44:4-5 (chamberlains are integral to the protagonist's rise to prominence)
Esther 1:12, 19-21, 7:7; Genesis 39:19-20 (ruler's burning anger leads to judgment)
Esther 2:3-4, 8-9; Genesis 41:34-37 (the ruler is pleased to appoint commissioners to do his bidding which in turn leads to the salvation of God's people by the promotion of the central figure of the narrative)
Esther 2:9, 9:19-22; Genesis 43:34 (generous portions)
Esther 2:12; Genesis 50:3 (fulfilled days)
Esther 2:21-23, 7:10; Genesis 40:22 (hanging as a pivotal feature in the narrative)
Esther 3:4; Genesis 39:10 (day after day refusal to listen)
Esther 3:10, 8:2; Genesis 41:42 (symbolism of the signet ring)
Esther 4:1, 3; Genesis 37:34 (sackcloth and mourning)
Esther 4:14; Genesis 45:5-7 (the reason the central figure was put in position of power is revealed)
Esther 4:16; Genesis 43:14 (if I [perish/am bereaved], I [perish/am bereaved])
Esther 5:2; Genesis 39:4, 21 (favor obtained)
Esther 6:1ff.; Genesis 41:1ff. (turning point revolves around the ruler's restlessness)
Esther 6:7-11, 8:15; Genesis 41:42-43 (robes, linen, gold, and a signet ring as kingly reward for salvific service)
Esther 6:14-7:10; Genesis 43:15ff. (guests escorted to the feast beginning the denouement)
Esther 7:8; Genesis 39:14 (household assault suspected)
Esther 8:6; Genesis 44:34 (for how can I see the [destruction of my kindred/evil that shall come upon my father])
Esther 9:4, 10:2-3; Genesis 41:40-43 (protagonist becomes second in command)
Esther 9:16ff.; Genesis 41:1ff., 47:30, 50:10 (allusions to Sabbatical rest)
What can be inferred? In both instances, God orchestrated events to display His power. In the Joseph narrative, Joseph is left to die in a pit, was sold into slavery, becomes successful as an officer's hand only to be thrown into jail; in Esther, the Jews were collectively decreed to be exterminated in the name of the very king whom Mordecai, a Jew, saved. Yet it was only by putting His divinely appointed vessels at such lows that God could demonstrate the extent and profundity of His sovereignty in its fullness. God protects His people and will give them rest from and victory over their enemies.