Idea from T34603: search around MediaWiki for "remove after 1.XX release" code and similar and kill that code (or file bugs to remember to remove the code later).
Make sure you use a commit summary that explains what you're doing/removing (reusing this task title isn't a good one!), and also add an entry to RELEASE-NOTES-1.29 similar to those that exist already https://github.com/wikimedia/mediawiki/blob/2c74b04/RELEASE-NOTES-1.29#L54-L68
Example: https://www.mediawiki.org/wiki/Special:Code/MediaWiki/104318 added "Do not release 1.19 with this." in a comment. Search for phrases like that.
List of things that could be removed (thanks to @Matthewrbowker):
Remove after...
<None found>
Deprecated, use ... instead
class ResetUserTokens
Skin::doEditSectionLink()
User::getImplicitGroups()
@deprecated (Soft deprecated)
class ProfileSection
function wfProfileIn() (ProfilerFunctions.php)
function wfProfileOut() (ProfilerFunctions.php)
class SpecialResetTokens
EDIT_TOKEN_SUFFIX (in User.php)
User::randomPassword()
User::setPassword()
User::setInternalPassword()
User::setNewpassword()
User::getTokenFromOption()
User::setCookie()
User::clearCookie()
User::setExtendedLoginCookie()
User::checkPassword()
User::checkTemporaryPassword()
User::getEditTokenTimestamp()
User::addNewUserLogEntry()
User::addNewUserLogEntryAutoCreate()
BufferingStatsdDataFactory::getBuffer()
User::getPasswordFactory()
User::passwordChangeInputAttribs()
Language::initEncoding()
Language::recodeForEdit()
Language::recodeInput()
Interwiki::isValidInterwiki()
Interwiki::fetch()
Inetwiki::getAllPrefixes()
class AuthManagerAuthPlugin
Class AuthManagerAuthPluginUser
Status::getErrorsArray()
Status::getWarningsArray()
$mUniqPrefix (in class Parser)
Parser::getRandomString()
Parser::uniqPrefix()
Parser::disableCache()
SkinFactory::getDefaultInstance()
ApiQueryInfo::getTokenFunctions()
ApiQueryInfo::resetTokenCache()
ApiQueryInfo::getEditToken()
ApiQueryInfo::getDeleteToken()
ApiQueryInfo::getProtectToken()
ApiQueryInfo::getMoveToken()
ApiQueryInfo::getBlockToken()
ApiQueryInfo::getUnblockToken()
ApiQueryInfo::getEmailToken()
ApiQueryInfo::getImportToken()
ApiQueryInfo::getWatchToken()
ApiQueryInfo::getOptionsToken()
LoadBalancer::getLaggedSlaveMode()
LoadBalancer::laggedSlaveUsed()
MimeMagic::singleton()
class ApiTokens
wfDeprecated (Hard deprecated)
Parser::getRandomString()
Parser::uniqPrefix()
$uniq_prefix in Parser::extractTagsAndParams()
ApiQueryLogEvents::addLogParams()
In DifferenceEngine::textDiff() there is a notation deprecating a variable
$wgSessionsInObjectCache in class Setup
SearchEngine::getOpenSearchTemplate()
WikiImproter::__construct() without a Config instance
LoginSignupSpecialPage::getFakeTemplate() has hook references depricated
ChangeTags::listExtensionActivatedTags()
ChangeTags::listExtensionDefinedTags()
VFormHTMLForm::isVForm()
User::setCookie()
User::clearCookie()
User::setExtendedLoginCookie()
ApiPageSet::getInvalidTitles()
User::createNew()
User::getEditTokenTimestamp()
User::getPasswordFactory()
Revision::getRawUser()
Revision::getRawUserText()
Revision::getRawComment()
MWLBFactory::getLBFactoryClass() (inside the class)
Class LoginForm
Job::batchInsert()
UploadBase::stashFileGetKey()
UploadBase::stashSession()
MWExceptionHandler::getLogId()
ApiResult::__construct - handing instance of ApiMain
ApiBase::getModuleProfileName()
ApiBase::safeProfileOut()
ApiBase::getProfileTime()
ApiBase::profileDBIn()
ApiBase::profileDBOut()
ApiBase::getProfileDBTime()
ResourceLoader::readStyleFiles() without a ResourceLoader context.
SpecialPageFactory::getList()
SpecialPageFactory::getPage() - Array syntax
StripState::__construct called with any arguements
GlobalFunctions.php - wfErrorLog()
GlobalFuctions.php - wfFixSessionID()
GlobalFunctions.php - wfResetSessionID()
GlobalFunctions.php - wfSetupSession()
Linker::getLinkColour()
Linker::link() with $query as string
SkinTemplate::outputPage() (Not sure on this one, it's hidden in an if())
Linker::formatTemplates()
MailAddress::__construct() called with a user object
Block::__construct with multiple arguements
OutputPage::__construct with no context
OutputPage::addExtensionStyle()
OutputPage::getExtStyle()
HTMLForm::isVForm()