Well....

1 The British sent another offer to moderate the dispute. It was passed along by Germany, but the German foreign secretary deliberately omitted a key bit...

That blows my mind completely.  First the German foreign secretary (along with the chancellor) lied to the Kaiser about the severity of the situation, then he lied again, by omission, to the Austro-Hungarian emperor, effectively torpedoing the last chance to avoid the carnage. What the hell was he playing at? Did he want a war?

People are complaining (and rightfully so) at the antics that some high-ranking members of the Obama administration have been engaging in lately.  As bad as those high crimes and misdemeanours are, though, they pale in comparison to helping to trigger a global war.  Never mind impeachment--IMO, the German foreign secretary deserved to hang.

2 One of the reasons the most recent post on the first shot fired is so short is that there seems to be some debate about what exactly was going on between the 27th and 29th. 
It does appear that the German Chancellor and some members of the General staff considered this to be both the ideal opportunity and last chance to take out France and Russia, which having just signed an alliance would represent an existential threat n a few years should they attack at once. 
Likewise, some in the Austrian court considered Serbia a threat out of all proportion ti its actual power because it was giving aid and comfort to ethnic secessionist movements in Bosnia that threatened to tear the empire apart. The big tipping point here was the Foreign Minister.
Emperor Franz Joseph was no pacifist. He'd fought in previous wars for long enough that he remembered when being commander in chief involved riding on a horse with a sword in front of the troops. However all those wars had given him a deep appreciation of how awful war was so he picked a very dovish man for foreign minister, a fellow named Berchtold (actually Leopold (Anton Johann Sigismund Josef Korsinus Ferdinand) Graf Berchtold von und zu Ungarschitz, Frättling und Püllütz  . He was mister peace and love until the two Balkan wars and was deeply humiliated by the fact that his peace efforts had failed and was widely derided as a result. Franz Joseph kept him on precisely because he had worked so tirelessly for peace on the grounds that that was not a bad trait for head diplomat. 
However, after 1912 Berchtold decided that peace with Serbia was a fools errand and the best way to secure stability was to completely conquer the Balkans, or at least Serbia. He secretly became a staunch ally of the most hawkish elements of the general staff. He worded the letter to the Serbs in such a way they had to reject it (Franz Joseph seems to have been appalled when he saw the final draft after the fact). The Emperor did not expect Mr. Peace to be the one who would conspire to bring about a war.
It does seem that Berchtold and the German chancellor were working to thwart any mediation offers. In fact the Austrian voices of restraint came mainly from members of the general staff concerned that an adventure in Serbia would bring about a war with Russia and possibly a far larger war. Berchtold ignored warnings about Russia, in part because of his monomaniacal focus on wiping out Serbia, which stemmed from his public ridicule for his pacifist views. 
The petty pique of a bureaucrat  can cause a great deal of grief. 
(Interestingly Berchtold did not stop being pacifistic on non-Serbian matters. He later offered a non trivial chunk of Austrian territory to the Italians in exchange for their not reneging on their treaty and invading Austria. This exceeding of his authority as well as his total failure to stop total catastrophe got him sacked a few months after the war started).