Now, I'd better stick in a disclaimer that Jamie is a real theologian - I'm just a nerd who reads too much. Anyway, as I note in his comment boxes, my understanding is that both acts are purely symbolic and relate to two intimately related aspects of the Papacy - the Pope as Universal Pastor and the Pope as Bishop of Rome. This second ceremony whereby he takes possesion of the Lateran is symbolic of his role as Ordinary of the Diocese of Rome. However, it should be noted that (to the best of my knowledge) neither ceremony has any jurdical effect. (This in in contrast with the fact that other diocesan bishops have to 'take canonical possession' of their diocese before their exercise their power to govern.)
This touches on an interesting point - in the run up to the election of Pope Benedict XVI it was (correctly) noted on the blogosphere that as soon as the chosen candidate accepted the Papacy he was Pope and had the supreme power of governance within the Church. However, this presumed that the chosen candidate was a Bishop, for the 1983 Code of Canon Law says:
Can. 332 §1. The Roman Pontiff obtains full and supreme power in the Church by his acceptance of legitimate election together with episcopal consecration. Therefore, a person elected to the supreme pontificate who is marked with episcopal character obtains this power from the moment of acceptance. If the person elected lacks episcopal character, however, he is to be ordained a bishop immediately.However, the 1917 Code of Canon Law stated that the one elected assumed the fullness of Papal power immediately, even if not already a bishop. The last time a non-Bishop was elected Pope was in the case of Pope Gregory XVI who was consecrated bishop 4 days after election. Even more interesting is the case of Pope Hadrian V - he was elected as a Deacon, his reign was only about 2 months long and in that period he didn't receive episcopal ordination. However, he certainly exercised the full powers of the Papacy by overturning the constitution regarding conclaves put into place by his predecessor Gregory X.
This points to an interesting question - the relationship between the sacrament of Holy Orders and the power to exercise jurisdiction within the church. When we bring in the cases of laymen being assigned dioceses and abbeys in the Middle Ages, the power wielded by certain 'mitred abbesses' and abbesses of 'double monasteries' and the fact that some of the 'Prince Bishops' in Germany were not always ordained bishop we see that historically there have been disjunctions between the power of governance and the sacrament of orders. Of course, contrary to what some theologian of a liberal stripe might say, that's not prima facie a good thing - the fact that certain pastoral offices were held by laity to the spiritual detriment of their subjects was amongst the causes of the Reformation.
Anyway, it is evident from history that a non-bishop elected to the Papacy may exercise Papal power. It is also obvious that it is supremely fitting that the Pope be an ordained bishop. However, what is at question is how much of this may be regulated by Canon law? Some theologians would argue that by Divine Law the one elected receives the jurisdiction of Pope immediately, even if not a bishop. Other theologians argue that this is merely ecclesiastical law - it is for the Church (through the laws made by preceding pontiffs) to lay down the rules as to when a man who is elected Pope assumes authority. It would seem that the 1983 Code settles the matter in favour of the latter position - however, the commentaries I have consulted say that the Canon was not intended to solve this theologial question and instead intended to put into place a practical norm that the one elected be ordained bishop as soon as possible.