Judges 1

1 Joshua did not train another man to lead Israel after he died. The people were to look directly to God for help. The people went to the priests who had the Urim and Thummim that God had chosen to communicate His wishes through (Exo 28:30).
2 God encouraged them to continue to take the land, but He did not make specific plans for them. When we read the Bible, God gives us many guidelines to live a happy, successful, and godly life, but He does not give us specific details like what our work should be, who we should marry, etc.
3 The tribes of Judah and Simeon are the first to be obedient. They join forces to clear out the land they had been allotted.
4 God rewarded their quick obedience with victory, just as He had promised.
7 The defeated king had cruelly injured and humiliated those he had defeated. In retribution, he suffered in a similar fashion. Presumably he was in prison until the time he dies. No other survivors are mentioned, so it appears that Judah and Simeon had followed the command to wipe out all the inhabitants.
8 Jerusalem was an important capital in those days and belonged to the Jebusites. Judah had earlier found that they could not dislodge the Jebusites by themselves, but with the help of Simeon they were able to (Josh 15:63). However, the victory was short lived as the remaining Jebusites rebuilt Jerusalem and held it until the time of David (Judg 1:21, 2 Sam 5:6-7).
12 We don't know why Caleb made this contest. Perhaps he had been frustrated on previous occasions by the people of Kiriath-sepher. Perhaps he had spent so much time in battle that he had not taken the time to find a suitable husband for his daughter.
13 It appears that a man could marry his niece and not break the marriage restrictions in Lev 18.
15 As an aside, Caleb needed to specifically designate what water sources Kenaz and his family had rights to.
16 Moses' father-in-law had been a pagan priest that later came to trust God. It appears his entire family accepted God and lived with Judah, even though Moses had come from the tribe of Levi. It appears that the Kenites did not merge with Israel, but they remained on friendly terms (Judg 4).
19 Joshua had told Judah that they could defeat the army of iron chariots, but for some reason they forgot the power of God and were too afraid to fight on their own (Josh 17:16). It was not until the time of Deborah that the army of iron chariots was defeated (Judg 4:1-15).
20 See Deu 1:35-36.
21 See Judg 1:8.
24 Rahab had been spared because she feared God (Josh 2:9-14). It appears that the man here feared the Israelites and committed treason only to save his own skin, not because he was turning against the evil of his pagan town.
25 This would be a strange city indeed if the main entrance was not apparent. However, I suspect that this "entrance" was a less used "back door" (e.g., to a well) or a secret passage meant for an escape route.
26 Unlike Rahab, this man did not join the Israelites. Instead, he moved away and built a new city. He named it Luz in memory of the town that he had betrayed.
28 God had specifically commanded that the Israelites drive the pagan inhabitants out of the land. Either because of complacency or lack of faith this command was not completed. The Israelites were also to be different from their former Egyptian oppressors, yet here we see them imitating the Egyptians by driving an entire nation into forced labor.
29 There are several other verses here indicating that various tribes allowed Canaanites to live among them. This would later turn out to be costly to Israel because the Canaanites would influence them to sin and bring God's judgment upon them.
34 In this case, not driving out the enemy had an immediate consequence. The others would face their consequences more slowly. The same is true today. If we do not obey God's commands fully we may suffer sooner or later, but we will suffer.