My observations from Rodric Braithwaite's 'Afgantsy', which is by no means the most comprehensive or detailed work on the conflict:
The strategic decision making behind entering Afghanistan wasn't great to begin with. In a way it was typical in that the Politburo members underestimated how big of a commitment the conflict would require in terms of time, resources etc.
Another political problem was the Soviets were tied to a regime that had become increasingly unpopular due to its policies and brutality. Some people benefited from its modernising policies, but many more found this to be an attack on their way of live which they got little benefit from. Its tendency towards brutalising any kind of opposition, even within the Afghan Communist party, only entrenched opposition. The Soviets replaced the previous leadership on arrival (Operation Storm 333), but the damage was already done and in some respects not enough changed.
Without a 'functional' local partner, a political solution wasn't effectively available. It is near impossible to end an insurgency using only military means, because without addressing those grievances etc. the rebels can keep recruiting or otherwise regenerate (so you might annihilate Group A, but a few years later a new Group B emerges because people are still unhappy). The local forces were also a mixed bag in terms of military support, which meant the comparitively small number of Soviet troops were having to 'cover' a huge area.
The Soviet entry into the war if anything expanded the opposition's base. What was once a fight with the government over its policies, became one about fighting a foreign invader. Areas that had previously been relatively 'safe' like in the north of Afghanistan became overrun with insurgents.
The Soviet military wasn't particularly well suited to this style of warfare. Much like the US military turned up to Vietnam with a skill set based around a European war, the Soviet Army didn't have the sort of doctine needed to hunt down insurgents and secure ground. While a fair bit of effort was put into adapting, for example by deploying recon and spetsnaz troops on operate against insurgents along the border with Pakistan, it wasn't really enough. So the standard pattern was to conduct large sweeps of insurgent areas, which would clear the area temporarily at sometimes high cost, then see the insurgents return after the military moved on.
The ability for some (all?) to have a safe area in Pakistan was handy, as was the ability to get supplies from there. The border area was also off limts to the military, probably to avoid an escalation of the conflict (some Pakistani leaders tended to see the Soviet invasion of Afghanistan as a prelude to an attack against their country). This resulted in strongholds like Krer being established by the insurgents. An operation by the spetsnaz against Krer, against orders, ended up being pretty disasterous however.
The mountainous terrain of Afghanistan was always going to make things difficult for the Soviets, and easier for the insurgents. Mountains mean lots of hiding places and harder to move troops though it which means harder to pursue insurgents. Never mind armoured vehicles having a hard time - which again runs into the doctrine issue.
Overall a minor issue, but one worth repeating - Soviet tanks didn't have good elevation on their main guns. This was related to the shape of their tanks (low profile turrets for example) and assumptions about what would be required for those vehicles in the event of war. This made it difficult for tanks in convoys or during operations to engage insurgent positions that were higher up. The same issue recurred in Chechnya, with the tanks unable to effectively hit insurgents bunkered in basements. The Soviets tried to compensate for this by making use of the ZSU-23 in a support role - being an anti-aircraft weapon it could naturally elevate its guns better.