TM1 only supports a certain number of functions from the complete MDX specification. Different versions of TM1 will support different functions (and potentially support the in different ways). The valid set of functions for the version of TM1 that you are using can be found in the main Help file, under Reference Material / MDX Function Support. Before trying to write a new query, make sure it is supported, and although some unlisted functions certainly do work they must be used at your own risk. The standard error message which means the function is genuinely not supported by your version of TM1 is, "Failed to compile expression".

One word of warning: by its very nature, the results of a dynamic subset can change. When including dynamic subsets in views, processes, SUBNM functions, and so forth, consider carefully what the potential future results might be, especially if the subset could one day be empty.

The two most common methods to go about actually creating a dynamic subset are to create them by hand or using TurboIntegrator.

By hand. You can either type (or paste) a query into the Expression Window as explained earlier, or you can choose Tools / Record Expression (and then Stop Recording when done) to turn on a kind of video recorder. You can then use the normal features of the subset editor (e.g. select by level, sort descending, etc.) and this recorder will turn your actions into a valid MDX expression. This is a great way to see some examples of valid syntax, especially for more complex queries.

When you have been recording an expression and choose Stop Recording TM1 will ask you to confirm if you wish to attach the expression with the subset - make sure to say ‘Yes’ and tick the ‘Save Expression’ checkbox when saving the resulting subset, otherwise only a static list of the result is saved, not the dynamic query itself.

Using TurboIntegrator. Only one line, using SubsetCreateByMDX, is needed to create and define the subset. You will need to know what query you want as the definition already. Note that the query can be built up in the TI script using text concatenation so can incorporate variables from your script and allow long queries to be built up in stages which are easier to read and maintain.
SubsetCreatebyMDX('Base Products','{TM1FILTERBYLEVEL({TM1SUBSETALL( [Product] )}, 0)}');
All TI-created MDX subsets are saved as dynamic MDX queries automatically and not as a static list.

Note that, at least up to TM1 v9.0 SP3, MDX-based subsets cannot be destroyed (SubsetDestroy) if they are being used by a public view, and they cannot be recreated by using a second SubsetCreateByMDX command. Therefore it is difficult to amend MDX-based subsets using TI. While the dynamic nature of the subset definition may make it somewhat unlikely you will actually want to do this, it is important to bear in mind. If you need to change some aspect of the query (e.g. a TM1FilterByPattern from “2006-12*” to “2007-01*” you may have to define the query to use external parameters, as documented in this document. This will have a small performance impact over the simpler hardcoded version.

Also, filter against values of a cube with SubsetCreateByMDX in the Epilog tab e.g. {FILTER({TM1FILTERBYLEVEL( {TM1SUBSETALL( [Product] )}, 0)},[Test].([Posting Measures].[Amount]) > 0 )} will not work if the values happen to have been loaded in the Data tab. You need to execute the SubsetCreateByMDX command in a subsequent TI process.

Note that TI has a limit of 256 characters for defining MDX subsets, at least up to v9.1 SP3, which can be quite limiting.