relatedTo 'and' with 'or'
You can simply get all the relevant categories at once and combine your relatedTo parameters with a single and operator:

{% set issue = craft.entries({ section: 'issues', slug: 'october-2014' }).first() %}
{% set categories = craft.categories({ group: 'articles', slug: 'category-slug-one, category-slug-two, category-slug-three' }) %}

{% set entries = craft.entries({
    section: 'articles',
    relatedTo: [
        'and',
        { targetElement: issue },
        { targetElement: categories }
    ]
}) %}