This is a hugely controversial issue with a number of different interpretations from major historians.

To start with, of the three, the Balfour declaration was the only one made for public consumption. The Sykes-Picot agreement was revealed by the Bolsheviks after the separate peace with Germany. Hussein-McMahon was first published in its entirety by George Antonius in the 30s from a translation of the Arabic originals.

Part of the issue for how this state of affairs came about has to do with how British foreign policy worked in the period and during the war. In theory, prosecution of the war was divided by the British between the Indian office and Egypt. Hussein McMahon was the first one negotiated, and the Egypt was given an enormous amount of discretion to negotiate with the Sharif of Mecca. It must be remembered that this is a wartime document, being negotiated under pressure, by a relatively minor civil servant, and the document reflects that. Sykes-Picot was a product of the foreign office, while the Balfour declaration came straight out of the cabinet. The level of coordination between these offices in each instant was minimal aside from generally following the plan laid out by the DeBunsen commission of 1915.

Sykes Picot was negotiated later. It has been argued that Sykes Picot was a British French attempt to actually carry out the intentions of the Hussein McMahon correspondences, but reflecting the fact that the Arab revolt was directly the product of European support and could not be sustained without that support. In other words, Hussein McMahon promised land for victory, when that victory failed to materialize, the allies negotiated Sykes-Picot. Again, this is a hugely controversial issue.

The Balfour declaration is almost an entirely different question. The issue is that the British promised a national homeland to the Jews but also stated that this would in no way prejudice pre-existing Palestinian status. It's not clear that they thought these claims were inherently contradictory at the time, but as the years progressed this was certainly made so. It's also the "strangest" in that unlike the Arab revolt or the British/French alliance there was no actual group whose support could be gained by this to win the war. One explanation comes in Tom Segev's "One Palestine, Complete" which posits that the British cabinet actually believed in a Jewish control of major industrial sectors as well as American influence and thought supporting Zionism would benefit them. Several cabinet members and the Prime Minister also seem to have, through their own Christianity, simply been sympathetic to the cause.

Faisal famously promised the Zionists that he would uphold the Balfour declaration so long as the British upheld Hussein McMahon. Obviously they didn't.

Another interpretation is that, in point of fact, the mandate system that was eventually carried out was not a reflection of Sykes-Picot. That British/French hegemony was not the same as British/French rule as envision by Sykes Picot. The British might have allowed themselves to believe this, in that they allowed Faisal, at first, to control Syria, then Iraq. Abdullah to control Jordan and possibly later to rule Palestine and Syria, and Hussein to rule the Hejaz. Only Iraq and Transjordan ended up with Hashemite control in the end.

Yet again, by the end of the war a number of British policy makers were apparently quite skeptical of the ability of Arab states to attain independence without British/French support, including T.E. Lawrence and Gertrude Bell.

In short, the negotiations were a mess, taken as a war time measure, and reflective of a bureaucracy that was poorly coordinated. The meaning of British promises and the extent to which they upheld them is a hugely debated issue and one that will continue to provide historical fodder probably til kingdom come.

Sources: One of the most interesting sources is Balfours 1919 memorandum, shortly before he resigned, summarizing British negotiations over the past five years and is excellent in how frank it is. Balfour clearly recognized that there was a serious problem at hand: http://www.scribd.com/doc/60431057/Memorandum-by-Mr-Balfour-Paris-Respecting-Syria-Palestine-And-mia

The best work I've come across, which is extremely readable and summarizes the various positions and negotiations made is D.K. Fieldhouse's "Western Imperialism in the Middle East, 1914-1958."

edit: full apologies in that I've written this rather quickly and it's still quite long and I'm not sure that I've specifically answered your question. It's quite a large question, and although I've read a lot on this topic I've barely scratched the surface. Source wise another interesting document are the notes of the Council of Four in 1919, which are less explicit than Balfour's memo, but show the kind of alliance level negotiation that was going on: http://digicoll.library.wisc.edu/cgi-bin/FRUS/FRUS-idx?type=turn&entity=FRUS.FRUS1919Parisv05.p0011&id=FRUS.FRUS1919Parisv05&isize=M

Obviously if anyone else has more to add please do so. And let me know if you have any questions about anything more specific and I'll try to answer it.