Firstly, the note claims a rather high level of statistical confidence, over 4σ, which is greater that 99% confidence. In particle physics, the general standard is that 3σ is considered evidence, while 5σ is called a discovery (a probability of the null hypothesis being true of 1 in a million); this means that, if correct, this group had almost enough data to claim to having found the particle.
Secondly, this note should not have been out. At CERN, there are internal notes such as this one that are not published in journals but remain within the confines of CERN researchers. This is in part to prevent bad papers from getting published with the CERN label, and it also means that the machine and experimentalist experts get the first crack at trying to find holes in a given analysis. That this note was leaked broke protocol, and there has been a fair bit of anger amongst the big shots.
Thirdly, the note is probably wrong in its assessment. Most are skeptical of this result and see it as a likely effect from a particle method of analysis. If you try a bunch of different ways to get a result from the data, eventually one will make nice plots, but then you may be simply fishing for anomalies. XKCD nailed that point recently. Moreover, such a high level of confidence when the LHC hasn't being running long and has not produced that much data from collisions strikes me as erroneous. I cannot be certain, but it really does force one to be skeptical.
Fourthly, even with 5σ confidence from one detector, without that being replicated at another detector at CERN it will be hard to truly claim that the Higgs has been found. One renegade group and/or leaker won't be able to take the prize so easily. Of course, some groups may be working much harder to make the discovery and don't want the credit shared with others that may not have done their part as competently, but ego isn't a great way to ensure good results. Enthusiasm is wonderful, zeal is powerful, but boastful pride will more likely cause problems. Fortunately, science is a community effort, so such hiccups in protocol is hardly going to taint future efforts. More likely, everyone else is going to be extra careful so they don't have to stand out in the cold alone.
The LHC is up and running again, and it is taking data faster than ever before. Who knows, we may actually make the discovery of this particle (or perhaps more than one Higgs particle?) in a year or two. No matter the result, it will point to the future of high energy physics. I'm 5σ confident.