Well, if Hitler had a bit more patience when AG north started the offensive in September and moved troops from the central front instead of the other way around Leningrad might have been captured. From wikipedia: "At this stage, Hitler ordered the final destruction of Leningrad with no prisoners taken, and on 9 September, Army Group North began the final push. Within ten days it had advanced within 11 kilometres (6.8 miles) of the city.
[263] However, the push over the last 10 km (6.2 mi) proved very slow and casualties mounted. Hitler, now out of patience, ordered that Leningrad should not be stormed, but rather starved into submission. "
If Leningrad falls then the Germans can anchor their northern flank on lake Ladoga and get a secure flank to attack toward Moscow. Sieging Moscow is better than capture the city outright. Why? Well, do what Ceasar did at Alesia and have a blocking force inwards and a larger force outwards to take care of the probable Soviet relief attempt.