We also hear that Caesar had an epileptic attack, which must have put quite an edge to the voice of the speakers as well. The anxiety and "edginess" in these scenes lead nicely to the more dramatic scene of the storm in Scene 3.

You really need to look at scene three to get the true picture of act one.  The first two scenes are excellent introduction scenes, but mood certainly isn't a focal point.  As scene three opens, we have two conspirators out wandering through a storm riddled night contemplating the fate of Rome under Julius Caesar.  The storm is a significant show of the ominous thoughts of the conspirators: bad things are afoot!  We have a small feeling of uncertainty about whether or not they will be successful in recruiting Brutus to join the faction; however, by this time Cassius has been established a shrewd manipulator and we fully expect him to be successful in landing Brutus as an ally.  By the end of act one, our mood is bordering suspense, but not quite there.  The assassination of Caesar is still a distant thought because of the importance of gaining Brutus's support first.

In the first act of the play, the Roman people are enjoying a holiday from work as they await Caesar's triumphant return to Rome after killing in battle the sons of Pompey, Rome's former ruler. They are clearly in a celebratory mood, taking nothing very seriously. Not everyone in Rome, however, celebrates Caesar's victory and his political power. In the opening scene, two tribunes--Flavius and Marullus--try to break up the crowds and clear the streets. Marullus scorns these common people, reminding them that they used to cheer for Pompey as they now support Caesar. He accuses them of terrible ingratitude. Marullus' comments suggest that the Roman people are easily swayed and very fickle in their loyalty to their leaders.

Later scenes, especially with Cassius and Brutus, show there is a growing concern among some in Rome about Caesar's rise to power and how he intends to use it. Brutus confides his concern to Cassius:

Brutus had rather be a villager

Than to repute himself a son of Rome

Under these hard conditions as this time

Is like to lay upon us.

Unlike the unthinking masses, Brutus fears that Caesar will make himself a king in Rome.

Well, the mood on the streets is riotous. Caesar has returned from a triumph against Pompey. The commoners are out on the streets celebrating his triumph. Yet he is so popular with the people that Cassius and Brutus are worried that Caesar might be chosen as a king - giving him a tyrannous power over Rome.

Even in the first scene, the mood of the commoners is split up by two malcontents, Flavius and Marullus:

Go you down that way towards the Capitol;
This way will I. Disrobe the images,
If you do find them deck'd with ceremonies.

Some people celebrate Caesar. Some are trying to limit his power. And that's true too of Brutus and Cassius. Antony is absolutely for Caesar:

When Caesar says 'do this' - it is performed.

Cassius, on the other hand, subtly goads Brutus into questioning Caesar's dominance over Rome, agreeing with him that they don't want Caesar to take the crown - but also asking why Caesar is so dominant:

'Brutus' and 'Caesar'. What should be in that 'Caesar'?
Why should that name be sounded more than yours?
Write them together: yours is as fair a name...

The political mood is clear: Caesar is becoming ever more powerful. And as he does so, more and more people are starting to wonder whether his power should not be limited. Flavius and Marullus, for pulling scarves off Caesar's images, are "put to silence". The conspiracy springs up secretly because any open opposition to Caesar will meet with their own solution to his power: death.

As the play opens, the citizens of Rome have taken to the streets to celebrate Caesar's triumphant return to Rome after defeating Pompey's sons in Spain. (Pompey had previously ruled in Rome.) Their mood is one of festivity and rejoicing as they enjoy a holiday from work. As the scene develops, Shakespeare presents these common people as being fickle in their loyalty to their leaders and easily swayed politically. Marullus, a Roman tribune, feels disgusted by their behavior and castigates them for their disloyalty, reminding them how they had once cheered for Pompey:

Many a time and oft 

Have you climbed up to walls and battlements,
To towers and windows, yea, to chimney tops,

Your infants in your arms, and there have sat

The livelong day with patient expectation

To see great Pompey pass the streets of Rome

Marullus tries to drive them from the streets, telling them a plague would surely descend on them for their great ingratitude. This theme, that the common people are politically disloyal and easily influenced, is emphasized in Act III when Antony turns the crowd against the conspirators by manipulating the crowd with his emotional oration. 

The fact that Marullus, as well as Flavius (another tribune), feels such anger at the crowd's behavior indicates that not everyone in Rome is pleased with Caesar's rise to power. Brutus' conversation with Cassius, which follows quickly in the plot sequence, makes clear the political division in Rome.

There is an ominous and foreboding mood in Act II, Scene 2 of Julius Caesar.

Certainly, the weather is ominous, as the thunder and lightning threaten in the heavens. Caesar himself observes, 

Nor heaven nor earth have been at peace tonight:
Thrice hath Calpurnia in her sleep cried out,
"Help, ho! They murder Caesar...." (2.2.1-3)

Shortly after his words, Calpurnia enters and reports ominous happenings that the watchman has witnessed--

• The watchman has seen "horrid sights" of a lioness whelping (giving birth) in the streets.
• Graves have opened and the dead issued forth with military formations coming from the clouds that then engaged in battle.
• Blood has drizzled down upon the Capitol and the din of battle clashed in the air.
• Horses have neighed and dying men groaned.
• Ghosts have screamed and shrieked in the streets. 

Caesar tells his wife that these omens can apply to rest of the world as well as to them. Yet, he expresses a certain fatalism:

...death, a necessary end,
Will come when it will come (2.2.36-37)

There are other omens, as well; for example, a servant reports that the augurers, religious officials in Rome who interpret and foretell events, have reported that a sacrificial animal had no heart in it. But, Caesar retorts that if he were to not go to the Senate House, he himself would be a beast without a heart. Still, Calpurnia begs her husband on this Ides of March to not go forth, but to send word that he is ill instead.

When Decius arrives in order to escort Caesar to the Senate, Caesar tells him of his wife's dream in which she saw his statue bleeding like a fountain while other Romans came toward this fountain, and with smiles on their faces, they bathed their hands in this blood. Caesar tells Decius, that Calpurnia considers this dream as an omen and begs her husband to stay home.
Decius interprets this dream in another manner, 

Your statue spouting blood in many pipes,
In which so many smiling Roman bathed,
Signifies that from you great Rome shall suck
Reviving blood, and that great men shall press
For tinctures, stains, relics, and cognizance. (2.2.85-89)

Decius here suggests to Caesar that people will beg for badges that indicate they are his servants; to the audience, he suggests that people will desire remembrances of his death. He has thus fed Caesar's ego. Further, Decius provokes Caesar into going to the Senate by asking,

If Caesar hid himself, shall they not whisper,
"Lo, Caesar if afraid?" (2.2.100-101)

Influenced by Decius, Caesar rejects Calpurnia's dream, as well as all the omens and disturbances of the heavens.  Therefore, when the others enter, among them Antony and Brutus, he departs for the Senate.