In Preludes and Nocturnes, in which Dream is captured, the reason for the mistake is not described. However, later in the Sandman series, during a flashback, Dream recalls his imprisonment, and hints that it occurred after a significant event, far from Earth, which he had attended. This event, or the lengthy journey back, had weakened him considerably, and he was returning in a vulnerable condition. It was only because of this vulnerability that the spell cast by Burgess was able to capture him, the implication being that it was a fluke that he was able to succeed even so far as getting one of the Endless at all. Death, it is implied, is far too powerful to fall to any mortal spell unless she deliberately limits her powers (which she does do occasionally; see Death: The High Cost of Living). It is also possible that the Magdalene Grimoire, the occult book used in the summoning ritual, was improperly employed, or that Burgess simply was not specific enough when he devised the ritual. Later stories employing the Magdalene Grimoire suggest that it is easily misused.
The question of intent is an interesting one. On the surface, Dream's capture was a simple accident, one he had to spend quite some time and effort to rectify. However, it was only because of his imprisonment that
his successor, Daniel, was brought into existence, by being gestated by Lyta Hall in the pocket dreamworld controlled by Brute and Glob.
As you had noticed, many events that seem random end up being used by Dream to his own ends. At the end of the series, when
Dream chooses to end his own existence by allowing the Furies to bring about his death, he seems aware that the child Daniel will take his place, as indicated by his gifting of the Eagle stone to Daniel before he departs. The duty-bound Dream may not have chosen to lay down his burden in the absence of a successor to pick it up.
Thus, the end of the series was dependent upon the beginning, an apparent accident and misfortune leading to the most powerful and pivotal event in the existence of the main character. I consider this both a highlight of Dream's foresight, and of the writing ability of Neil Gaiman. This arc also points out both Dream's strength and his weakness, for though he is powerful and timeless enough to foresee and use seemingly random events, ultimately he is not able to choose to step off of the path of consequences.