What to look out for/note/discuss

You could simplify this to the 4 technical areas you have to consider.

1. cinematography (camera work, shot types, angles, framing, movement)
2. editing (including transitions, SFX; linear or non-linear; (dis)continuity etc)
3. sound ((non-)diegetic; use of music [often signifies core target audience + genre - can also be clumsy and overused; say so if you think so]; audio bridge; voiceover etc)
4. mise-en-scene (includes props, locations, costume, makeup - verisimilitude?)

• intertextuality (links/references to existing texts)
• genre conventions observed ... or broken (very useful to note so you can find examples to look back on when designing your own work. you could also note hybridity here, where you see signifiers of 2 or more genres [to help widen audience appeal])
• how the opening concludes and the main movie resumes (the final shot of your opening is incredibly important, so its worth carefully noting these)
• particularly useful shots/details - if you see something you think is well done and you might want to take influence from its worth highlighting

• IDENTS: How long are they typically, how high-tech/complex; how many do we see; where do they appear
• TITLES: This is a key part of your overall coursework task, so detailed notes are important. Which roles/companies are noted; what specific language is used; do any names/companies appear more than once; what font (serif/sans-serif; colour; case) is used; note the positioning (does this differ between titles) and any animation; any graphic element to the titles; is there a gap between titles or do they continuously appear (eg company names - A Warp Films Production - a gap then individual credits?) Position
• OPENING SHOT: always worth noting. Any audio bridge linking it with idents? Most common shot is the extreme long shot. 
• RUNNING TIME OF OPENING: How long is the self-contained opening sequence? Is it clear where this ends?
• CLOSING SHOT OF OPENING + TRANSITION TO MAIN BODY OF FILM: Always note the final shot too. Do you get a fade-out or other transition or a straight cut? Are titles used to reinforce a change of location/time immediately after the opening ends? 
• EDITING: any transitions to signify ellipsis; any SFX; continuity editing style or any hallmarks of discontinuity?
• LENGTH OF TAKES + EDITING PACE: looooong takes or fast-paced editing with short takes? much variation in this? Simply by following one character/keeping referring back to them also suggests to the audience that they are a central character.
• SHOT VARIETY: ask yourself as you watch these whether you think further shots should be inserted - is there sufficient shot variety? This and the above point are linked. Look for simple things too like two-shots used to signify personal relationships.
• MISE-EN-SCENE: This links to the above point: what does the mise-en-scene communicate to the audience (providing exposition on location, time period, genre etc)? Is verisimilitudeachieved (can you see evidence of costuming, set-dressing, props etc)?
• SETUPS/SCENES: Each time you leave a room or other part of a location you have to work to setup the next scene: how many setups or scenes are involved?
• FLASHBACKS/MAJOR ELLIPSIS: Halloween is one of many that opens with events and then gives a title stating x years later so we know we're now in the present.
• NARRATIVE ENIGMA V EXPOSITION: What do we learn about setting, time period, narrative, characters, genre - and what is intentionally withheld? Do we appear to meet antagonist or protagonist/s? You could also comment here on plot, cliffhangers etc
• SOUND + MUSIC: Note use of diegetic (if its coming from the world on screen) and non-diegetic sound. Specifically, how is music used, if at all - is it continuous; are multiple music tracks used; does the volume level rise? Does the music genre seem to hint at the target audience and/or genre?
• GENRE SIGNIFIERS: Do you see anything which seems to point towards a particular genre?
• INTERTEXTUALITY: Are there references to existing texts?
• REPRESENTATIONS: Of Age and Gender. Use of stereotypes, countertypes, a mix of both? When looking at horror openings, be alert for stock characters like scream queens, masked killer, jock, nerd, final girl, ineffective adult/authority figure etc
• GENRE/BUDGET/ERA SPECIFIC? You'll find that conventions have changed over time and also vary with budget and genre.
• MEMORABLE ASPECTS: Quite simply, anything you thought was particularly interesting or noteworthy. Especially as you begin to work on horror openings, you should note where you see useful examples of costume, dialogue, editing etc which you may well take direct inspiration from.