PHB p145 only specifies "When a character achieves a new level, make these changes". The changes are not specified to occur in any specific order, although in some cases, there are obvious dependencies between the steps. The above longsword example is a good case for "no specific order aside from dependencies".
Here's another one:
If a character takes his 4th level, he is entitled to increase his stats by one. Supposing he increases his int by 1 at that level, does he get an extra skillpoint that level, or does that not take effect until next level? The PHB says absolutely nothing about this. This is of particular note because intelligence bonusses do not appear to be, at present, retroactive, and therefore, this subject is of great concern to anyone who plays a wizard.
Obviously, of course, a character not meeting the skillpoint requirements is unable to take the PrC, since he must meet the skill point requirements to take the class, and cannot allocate skill points until he has chosen a class to level up in, since that choice determines how many skillpoints he gets, and what his class and non-class skills are. A feat requirement is more dicey: If a character levels to an increment-of-3 level, he always, no matter what, gets to take a feat just by character level. Whether or not this feat taken would allow him to qualify for the PrC is unknown, although I'd be inclined to allow a feat gained at level-up to count, unless it's acquired as a bonus feat for a class, since class is indeterminate.
As above, the cleric example is generally accepted as legal by PHB p. 77, but contradicts the order of level-up upgrades. However, PHB p. 145 does not specify that those upgrades occur in any specific order, so, barring any undetermined quantities, PHB p. 77 clearly implies that they occur in whatever order is most beneficial.