Recognitions:

## Why is the magnetic field of a superconductor normally excluded?

No, the finite energy of the plasmons (irrespective of in the superconductor or normal metal) is due to the long range of the Coulomb forces. Screening does not work for this kind of collective modes.
The doubts on the validity of the BCS explanation of the Meissner effect spurred several important developments (I can give you references tomorrow).
For example Nambu wrote in his Nobel lecture ( http://www.nobelprize.org/nobel_priz...u-lecture.html )
"I will now recall the chain of events which led me to the idea of SSB and
its application to particle physics. One day in 1956 R. Schrieffer gave us a
seminar on what would come to be called the BCS theory [5] of supercon-
ductivity. I was impressed by the boldness of their ansatz for the state vector,
but at the same time I became worried about the fact that it did not appear
to respect gauge invariance. Soon thereafter Bogoliubov [6] and Valatin [7]
independently introduced the concept of quasiparticles as fermionic excita-
tions in the BCS medium. The quasiparticles did not carry a definite charge
as they were a superposition of electron and hole, with their proportion
depending on the momentum. How can one then trust the BCS theory for
discussing the electromagnetic properties like the Meissner effect? It actually
took two years for me to resolve the problem to my satisfaction. There were
a number of people who also addressed the same problem, but I wanted to
understand it in my own way. Essentially it is the presence of a massless col-
lective mode, now known by the generic name of Nambu-Goldstone (NG)
LPN 2008 ekvationer...
boson, that saves charge conservation or gauge invariance."

 Quote by DrDu No, the finite energy of the plasmons (irrespective of in the superconductor or normal metal) is due to the long range of the Coulomb forces. Screening does not work for this kind of collective modes.
I don't understand what you mean here. What collective modes? And how is screening supposed to work for "other modes" that it doesn't work for "these modes"?

 Quote by DrDu The doubts on the validity of the BCS explanation of the Meissner effect spurred several important developments (I can give you references tomorrow). For example Nambu wrote in his Nobel lecture ( http://www.nobelprize.org/nobel_priz...u-lecture.html ) "I will now recall the chain of events which led me to the idea of SSB and its application to particle physics. One day in 1956 R. Schrieffer gave us a seminar on what would come to be called the BCS theory [5] of supercon- ductivity. I was impressed by the boldness of their ansatz for the state vector, but at the same time I became worried about the fact that it did not appear to respect gauge invariance. Soon thereafter Bogoliubov [6] and Valatin [7] independently introduced the concept of quasiparticles as fermionic excita- tions in the BCS medium. The quasiparticles did not carry a definite charge as they were a superposition of electron and hole, with their proportion depending on the momentum. How can one then trust the BCS theory for discussing the electromagnetic properties like the Meissner effect? It actually took two years for me to resolve the problem to my satisfaction. There were a number of people who also addressed the same problem, but I wanted to understand it in my own way. Essentially it is the presence of a massless col- lective mode, now known by the generic name of Nambu-Goldstone (NG) LPN 2008 ekvationer... boson, that saves charge conservation or gauge invariance."
Yes, I remember reading his Nobel lecture. Let me emphasize once more that:
1. The flow of a supercurrent is not accompanied with excitations of any kind. Period. In fact, it may be accepted as a condition of superfluidity;
2. I think the BCS Hamiltonian is gauge invariant. It is true that the product:
$$c^{\dagger}_{\mathbf{k} \uparrow} \, c^{\dagger}_{-\mathbf{k}\downarrow}$$
gets a phase after a gauge transformation, but you have to remember that this product is itself multiplied by the gap function $\Delta(\mathbf{k})$, which in the BCS theory is given as the average:
$$\Delta(\mathbf{k}) = -\frac{1}{V} \, \sum_{\mathbf{q}}{\tilde{U}_{\mathbf{q}} \, \langle c_{\mathbf{k} + \mathbf{q}, \uparrow} \, c_{-\mathbf{k} + \mathbf{q},\downarrow} \rangle}$$
so, it acquires an opposite phase than the above product. These two phases cancel one another and the Hamiltonian is left gauge invariant.

Recognitions:
Before answering let me say that I mainly wanted to point out the historical perspective, namely how superconductors were found to be the first examples of systems in which the Higgs mechanism is at work.

 Quote by Dickfore I don't understand what you mean here. What collective modes? And how is screening supposed to work for "other modes" that it doesn't work for "these modes"?
Let me try to answer this question first: Plasmons are collective modes. They are responsible for the screening in metals and superconductors. However the plasmon cannot screen itself.

Second: In a superconductor global gauge symmetry is broken. Hence one would expect from Goldstones theorem some collective mode which zero frequency in the long wavelength limit, i.e. some collective excitation inside the gap.
It is clear that this may potentially render the analysis of BCS of the Meissner effect invalid, as with collective modes inside the gap there would be no gap and a paramagentic contribution to the current cannot be excluded.

However, there are no excitations inside the gap in a real superconductor. Anderson was (at least one of ) the first who showed that the Goldstone mode has a finite frequency also at k=0 once Coulomb interaction is taken into account and that it becomes a normal plasmonic mode which does not lie in the gap:
http://prola.aps.org/abstract/PR/v112/i6/p1900_1
http://prola.aps.org/abstract/PR/v110/i4/p827_1
Others who analyzed this situation where Rickayzen and Nambu.
Especially Nambu has worked out the mechanism much more clearly making use of the Ward identities: http://prola.aps.org/abstract/PR/v117/i3/p648_1
This whole analysis was spurred by the doubts about the validity of the calculation of the Meissner effect by BCS, let me cite here the abstract from the article by Schafroth
http://prola.aps.org/abstract/PR/v111/i1/p72_1
: "It is shown that a theory of superconductivity which starts from an "effective" Hamiltonian with significantly velocity-dependent interaction between electrons does not possess well-defined magnetic properties. The Meissner effect cannot therefore be established from such a theory. This applies in particular to the Bardeen-Cooper-Schrieffer theory."

At about the same time particle theorist were desperately seeking models of relativistic systems with broken symmetry but not possessing zero mass Goldstone boson.
Anderson wrote a paper in 1963
http://prola.aps.org/abstract/PR/v130/i1/p439_1
where he tried to explain the mechanism to particle theorists.
Higgs developed the first relativistic model showing the Higgs mechanism in response to the article by Anderson.