Will try to reply to both of these - Natrius - yes but not perfectly -
neurotech -
Yes and no I would say... Although your cardiothoracic surgeon may still disagree, and mine (I am a med student and work closely with cardiothoracic surgeons) may disagree with me also - it is really about degree. I would disagree that you can find more information out by a stethescope although bloods, the 'clinical picture' (what the patient looks like when they walk/get wheeled through the door) and ECG will all generally contribute - a stethoscope will not tell you about a heart attack, and an ECG will not necessarily inform you of valve abnormalities which is what you are listening to (although you may detect things like ventricular hypertrophy that are caused by Aortic Stenosis etc)

There is only so much useful information you can extract from an ECG. What I mean by this is that for the primary care physician, the information that you want to extract is: are they having a heart attack, do they have major electrolyte disturbances, do they have an abnormal rhythm that we need to shock them out of now; is there evidence of previous myocardial infarct? - these influence immediate management in the emergency room; if there are other abnormalities then if the problems are localised to the heart a cardiologist will generally be called, as, like any field, there is a significant degree of specialisation once you move beyond the specifics.

Natrius: what is a computer bad at? I'll try and explain as best I know how:
1st Degree heart block? Easy (P wave more than 200ms)
2nd degree heart block? again, fairly easy. just a matter of timing. computers can handle this easily as well as it is simply a measure of difference between 2 different amplitudes.

3rd degree heart block, again, pretty straight foreward.

Myocardial Infarct (heart attack) and ischaemia: relatively straightforward for a computer and human to read as there are 'voltage criteria' that determine if the heart is starved of oxygen or not; basically to do with the time for repolarisation of the heart muscle in the presence of 0 oxygen.

Systolic Tachycardias - straightforward and easy to see just vusually. Same with ventricular tachycardias.

Various electrolyte abnormalities - get a bit more difficult. different waves start to blend into each other. These can be quite non-specific and can mimic other abnormalities. Partially this is because they cause such strange changes to the electrical activity in the heart, which changes the de/repolarisation of the muscle, which changes the look of the electrical activity. also, shifts in one electrolyte will often lead to shifts in others, which further muddies the waters.

In general, The easy stuff (based on voltage criteria, times between peaks and troughs) etc is relatively well handled by computers; some aberrant rhythms trick them, and electrolyte changes or waves that look as if they are abnormal give the computer nowhere to go - it doesn't know what to call it so calls it 'abnormal rhythm' -
basically it would be up to the clinician to combine the clinical picture, ECG and blood results to get a diagnosis and correct.
additionally, ECG readings and interpretation may be complicated by previous infarcts, chest wall deformities, 'dextrocardia' - heart on the other side of the chest; about 1:10,000, and incorrect lead placement..
Can it be improved? Sure. In fact there are some studies that suggest that it might even be possible to predict heart attacks from fractal analysis of ECGs several days out from the actual event (this is kind of like fractal analysis of earthquakes and I know very little about it... neurotech you may perhaps know about some of this when used with EEGs? I have heard it is useful there too)

hope this helps your understanding