Old question & I know the original posters are inactive, but since it came up in a Google search, I thought I'd add my thoughts.
1) Make Start_Date and End_Date regular, atomic attributes (either
ISO8601 strings or the DB's datetime object) and only allow limitted
filtering.
Putting a date attribute into an existing dimension makes sense if the main goal is informational (i.e. people want to include the start/end date of the promotion in reports). However, if the intention is to filter, then filtering on an atomic date attribute will be relatively painful.
2) Make Start_Date and End_Date foreign keys to the Date table,
breaking the star schema, but allowing the same filtering capabilities
as the full Date dimension.
This type of snowflaking is called an Outrigger Dimension and can be acceptable in a star schema. (http://www.kimballgroup.com/data-warehouse-business-intelligence-resources/kimball-techniques/dimensional-modeling-techniques/outrigger-dimension/). I imagine this is what you did.
3) Include attributes like Start_Date_Day_of_Week, Start_Date_Quarter,
maintaining the star schema but increasing the dimension size and
essentially duplicating the structure of the Date dimension in the
Promotions dimension.
The duplication would get messy (maintaining multiple date fields, especially since you have multiple dates in the same dimension). It also makes future maintenance more complex: if you want to alter your date dimension, you have to repeat that alteration in dozens of places (or have an inconsistent user experience).
On the flip side, this might be a valid option if, for example, there are just one or two ways that you know people want to filter promotions on. For example, if you know end-users want to quickly filter to active promotions or "promotions closed in the last 30 days", you could calculate and add that as a specific attribute in the promotion dimension, rather than linking to a full date dimension for promotion start & end date. (Though what starts out as one or two attributes can expand quickly, as end-users find more and more time periods they want to filter to.)
There is a 4th and 5th option, depending on the specifics of what you intend to filter by promotion start/end dates:
4) Add the promotion start/end date fields as keys in the Sales table.
You'll be storing the same piece of information each time a promotion is used, so at first glance, it feels like a lot of duplication. But denormalization is the name of the game in a star schema. If your goal is to filter to sales based on the promotion start or end date (i.e. sales where the promotion start date was last month), I would recommend this over an outrigger dimension.
5) Create a new, factless fact table, for promotions
If your goal isn't to filter sales at all, then a factless fact table might be a better solution. This could tell you how many promotions were in effect on a given date (regardless of whether there were associated sales), for example. More information: http://www.kimballgroup.com/2011/04/design-tip-133-factless-fact-tables-for-simplification/
My experience with dimensional modeling is that the best solution often depends on what the end-user is trying to accomplish. If you (or they) are not yet sure what they're trying to accomplish (i.e. you know promotions have start & end dates and that's it), I'd start with option #1. This puts the information in your model without too much work.
If it later transpires end-users are trying to filter Sales by start & end dates, that's when I'd consider #2 or #4. If it transpires end-users are trying to analyze promotions independently of sales, I'd look at #5.
Typically dimensional modelling starts by identifying facts and the dimensions about those facts. Most of those things you mention are dimension attributes.
Staff/employees alone and their place in an organization is probably going to be modeled with a factless fact table.
You may well have a supervisor/employee relationship, and this would be an instance of a factless fact table where the facts in that table are likely to be dates of supervision (these are really a lot like degenerate dimensions).
However, I expect you will have fact tables like hours worked etc which will use these dimensions as foreign keys.
It is very unusual to be modeling dimensions in isolation, as dimensional modeling is a very pragmatic type of approach which is very dependent upon the type of data you have as well as the types of analysis. The choice of how many dimension tables and which attributes go in which dimensions is very dependent upon data behavior and can sometimes be quite arbitrary.
Best Answer
Absolute numbers for months and quarters allow them to sort correctly when used in a query tool. A 'month of year' value is only useful for sorting within a year, but an absolute month value that is in order will sort a list of months correctly across years. This is very helpful to support (for example) a report over a rolling 12 month period.
Keys for week, month or quarter (the year itself is inherently ordinal and suffices for this on years) also allow attributes such as day of month to be keyed to a logical key. Although the dimension table itself may be flat, many tools (OLAP servers, for example) will still impose a logical hierarchy within the data and require a key that is unique at its level to do this.