A friend of mine asked me once what I would suggest to church leaders who want to make changes to our culture that will attract more converts and retain more members. The following was my response - and I believe all of them could be accomplished without sacrificing important doctrine in any way:
1) Openly respect and acknowledge differences - that people can look and believe differently and still be considered faithful. Preach that from the General Conference pulpit fairly regularly until it's ingrained into the general membership, and use specific examples explicitly. (political affiliation, doctrinal understanding, facial hair, etc.)
2) Focus on making our meetings "revelatory opportunities", especially making Sacrament Meeting a spiritual worship service.
3) Emphasize "sharing the Gospel" by just talking naturally about our lives and inviting people to attend meetings and activities with us with no expectation of immediate conversion. Quit talking about "member missionary work" completely by substituting "sharing the Gospel". Encourage community service as the central aspect of ward and auxiliary activities - and stress service toward those whom we don't serve naturally.
4) Make it crystal clear that single adults can serve in ANY local calling in any ward or branch, except perhaps Bishop and Relief Society President. Encourage meaningful callings for Young Single Adults, including presidency positions - even if that means expanding to three counselors where possible.
5) Apply that same standard for celibate gay members, and make it clear to all members that homosexual attraction is not a sin or transgression in any way that would limit a person's ability to serve faithfully in the kingdom. That is the least we can do with regard to our gay brothers and sisters, even though there is more that could be done without sacrificing anything within our theology or core doctrinal framework.
6) Be much more open about soliciting input without any fear of negative consequence. Provide an online forum for anonymous input, if necessary - understanding the crap that will be said by many people but enduring it to get to the pearls of wisdom. Lacking that, mention explicitly profound things said in some of the largest Mormon group blogs.
As "secondary" but important policy changes:
7) Change the marriage policy to allow ALL members world-wide to marry civilly and publicly first and then be sealed in the temple privately. If it can be allowed in countries where it must be done that way, it can be allowed world-wide - and the serious issues associated with the current exclusion of family and friends who are not temple recommend holders would disappear if civil marriages were allowed prior to temple sealings.
I understand and have no problem with the concept of waiting to be sealed IF a couple is getting married as a result of pregnancy (the need to repent) or a couple simply chooses to get sealed whenever they feel like it (the existence of apathy), but those cases now constitute a much lower percentage of situations in our modern church. Again, if it can be allowed in some countries where it is required by law, without sacrificing anything that is doctrinally important, it can be allowed world-wide.
8) Revamp the temple recommend interview to reword some of the questions currently asked - especially the one about affiliation. That one simply is too ambiguous and can't be answered adequately as worded currently.